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University of Tech  Iraq  QMDS 10110
CHAPTER 10: TWOSAMPLE TESTS
1)The t test for the difference between the means of 2 independent populations assumes that the respective
sample sizes are equal
University of Tech  Iraq  QMDS 10110
CHAPTER 10: TWOSAMPLE TESTS
1)The t test for the difference between the means of 2 independent populations assumes that the respective
sample sizes are equal
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University of Tech  Iraq  QMDS 10110
CHAPTER 10: TWOSAMPLE TESTS
1)The t test for the difference between the means of 2 independent populations assumes that the respective

 sample sizes are equal.
 sample variances are equal.
 populations are approximately normal.
 All of the above.
 The t test for the mean difference between 2 related populations assumes that the
 population sizes are equal.
 sample variances are equal.
 population of differences is approximately normal or sample sizes are large enough.
 All of the above.
 If we are testing for the difference between the means of 2 related populations with samples of n_{1} = 20 and n_{2} = 20, the number of degrees of freedom is equal to
 39.
 38.
 19.
 18.
 If we are testing for the difference between the means of 2 independent populations presumes equal variances with samples of n_{1} = 20 and n_{2} = 20, the number of degrees of freedom is equal to
 39.
 38.
 19.
 18.
 In what type of test is the variable of interest the difference between the values of the observations rather than the observations themselves?
 A test for the equality of variances from 2 independent populations.
 A test for the difference between the means of 2 related populations.
 A test for the difference between the means of 2 independent populations.
 All of the above.
 In testing for the differences between the means of 2 independent populations where the variances in each population are unknown but assumed equal, the degrees of freedom are
 n – 1.
 n_{1} + n_{2} – 1.
 n_{1} + n_{2} – 2.
 n – 2.
 In testing for differences between the means of 2 related populations where the variance of the differences is unknown, the degrees of freedom are
 n – 1.
 n_{1} + n_{2} – 1.
 n_{1} + n_{2} – 2.
 n – 2.
 In testing for differences between the means of two related populations, the null hypothesis is
 .
 .
 .
 .
 In testing for differences between the means of two independent populations, the null hypothesis is:
 = 2.
 = 0.
 > 0.
 < 2.
 When testing for the difference between 2 population variances with sample sizes of n_{1} = 8 and n_{2} = 10, the number of degrees of freedom are
 8 and 10.
 7 and 9.
 18.
 16.
 The statistical distribution used for testing the difference between two population variances is the ___ distribution.
 t
 standardized normal
 binomial
 F
 The test for the equality of two population variances is based on
 the difference between the 2 sample variances.
 the ratio of the 2 sample variances.
 the difference between the 2 population variances.
 the difference between the sample variances divided by the difference between the sample means.
 True or False: The F test used for testing the difference in two population variances is always a onetailed test.
 In testing for the differences between the means of two related populations, the _______ hypothesis is the hypothesis of "no differences."
 In testing for the differences between the means of two related populations, we assume that the differences follow a _______ distribution.
 In testing for the differences between the means of two independent populations, we assume that the 2 populations each follow a _______ distribution.
 Given the following information, calculate the degrees of freedom that should be used in the pooledvariance t test.
s_{1}^{2} = 4 s_{2}^{2} = 6
n_{1} = 16 n_{2} = 25

 df = 41
 df = 39
 df = 16
 df = 25
 Given the following information, calculate s_{p}^{2}, the pooled sample variance that should be used in the pooledvariance t test.
s_{1}^{2} = 4 s_{2}^{2} = 6
n_{1} = 16 n_{2} = 25

 s_{p}^{2} = 6.00
 s_{p}^{2} = 5.00
 s_{p}^{2} = 5.23
 s_{p}^{2} = 4.00
TABLE 101
Are Japanese managers more motivated than American managers? A randomly selected group of each were administered the Sarnoff Survey of Attitudes Toward Life (SSATL), which measures motivation for upward mobility. The SSATL scores are summarized below.

American

Japanese

Sample Size

211

100

Mean SSATL Score

65.75

79.83

Population Std. Dev.

11.07

6.41

 Referring to Table 101, judging from the way the data were collected, which test would likely be most appropriate to employ?
 Paired t test
 Pooledvariance t test for the difference between two means
 Independent samples Z test for the difference between two means
 Related samples Z test for the mean difference
 Referring to Table 101, give the null and alternative hypotheses to determine if the average SSATL score of Japanese managers differs from the average SSATL score of American managers.
 Referring to Table 101, assuming the independent samples procedure was used, calculate the value of the test statistic.

 Referring to Table 101, suppose that the test statistic is Z = 2.45. Find the pvalue if we assume that the alternative hypothesis was a twotailed test ().
 0.0071
 0.0142
 0.4929
 0.9858
TABLE 102
A researcher randomly sampled 30 graduates of an MBA program and recorded data concerning their starting salaries. Of primary interest to the researcher was the effect of gender on starting salaries. Analysis of the mean salaries of the females and males in the sample is given below.
Hypothesized Difference

0

Level of Significance

0.05

Population 1 Sample

Sample Size

18

Sample Mean

48266.7

Sample Standard Deviation

13577.63

Population 2 Sample

Sample Size

12

Sample Mean

55000

Sample Standard Deviation

11741.29

Difference in Sample Means

6733.3

tTest Statistic

1.40193

LowerTail Test

Lower Critical Value

1.70113

pValue

0.085962

 Referring to Table 102, the researcher was attempting to show statistically that the female MBA graduates have a significantly lower mean starting salary than the male MBA graduates. According to the test run, which of the following is an appropriate alternative hypothesis?
 Referring to Table 102, the researcher was attempting to show statistically that the female MBA graduates have a significantly lower mean starting salary than the male MBA graduates. From the analysis in Table 102, the correct test statistic is:
 0.0860
 – 1.4019
 – 1.7011
 – 6,733.33
 Referring to Table 102, the researcher was attempting to show statistically that the female MBA graduates have a significantly lower mean starting salary than the male MBA graduates. The proper conclusion for this test is:
 At the = 0.10 level, there is sufficient evidence to indicate a difference in the mean starting salaries of male and female MBA graduates.
 At the = 0.10 level, there is sufficient evidence to indicate that females have a lower mean starting salary than male MBA graduates.
 At the = 0.10 level, there is sufficient evidence to indicate that females have a higher mean starting salary than male MBA graduates.
 At the = 0.10 level, there is insufficient evidence to indicate any difference in the mean starting salaries of male and female MBA graduates.
 Referring to Table 102, the researcher was attempting to show statistically that the female MBA graduates have a significantly lower mean starting salary than the male MBA graduates. What assumptions were necessary to conduct this hypothesis test?
 Both populations of salaries (male and female) must have approximate normal distributions.
 The population variances are approximately equal.
 The samples were randomly and independently selected.
 All of the above assumptions were necessary.
 Referring to Table 102, what is the 99% confidence interval estimate for the difference between two means?
 Referring to Table 102, what is the 95% confidence interval estimate for the difference between two means?
 Referring to Table 102, what is the 90% confidence interval estimate for the difference between two means?
TABLE 103
The use of preservatives by food processors has become a controversial issue. Suppose 2 preservatives are extensively tested and determined safe for use in meats. A processor wants to compare the preservatives for their effects on retarding spoilage. Suppose 15 cuts of fresh meat are treated with preservative A and 15 are treated with preservative B, and the number of hours until spoilage begins is recorded for each of the 30 cuts of meat. The results are summarized in the table below.
Preservative A Preservative B
_{A} = 106.4 hours _{B} = 96.54 hours
S_{ A} = 10.3 hours S_{ B} = 13.4 hours
 Referring to Table 103, state the test statistic for determining if the population variances differ for preservatives A and B.
 F = – 3.10
 F = 0.5908
 F = 0.7687
 F = 0.8250
 Referring to Table 103, what assumptions are necessary for a comparison of the population variances to be valid?
 Both sampled populations are normally distributed.
 Both samples are random and independent.
 Neither (a) nor (b) is necessary.
 Both (a) and (b) are necessary.
TABLE 104
A real estate company is interested in testing whether, on average, families in Gotham have been living in their current homes for less time than families in Metropolis have. Assume that the two population variances are equal. A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes.
Gotham: _{G} = 35 months, s_{G}^{2} = 900 Metropolis: _{M} = 50 months, s_{M}^{2} = 1050
 Referring to Table 104, which of the following represents the relevant hypotheses tested by the real estate company?
 Referring to Table 104, what is the estimated standard error of the difference between the 2 sample means?
 4.06
 5.61
 8.01
 16.00
 Referring to Table 104, what is an unbiased point estimate for the mean of the sampling distribution of the difference between the 2 sample means?
 – 22
 – 10
 – 15
 0
 Referring to Table 104, what is(are) the critical value(s) of the relevant hypothesis test if the level of significance is 0.05?
 t @ Z = – 1.645
 t @ Z = 1.96
 t @ Z = – 1.96
 t @ Z = – 2.080
 Referring to Table 104, what is(are) the critical value(s) of the relevant hypothesis test if the level of significance is 0.01?
 t @ Z = – 1.96
 t @ Z = 1.96
 t @ Z = – 2.080
 t @ Z = – 2.33
 Referring to Table 104, what is the standardized value of the estimate of the mean of the sampling distribution of the difference between sample means?
 – 8.75
 – 3.69
 – 2.33
 – 1.96
 Referring to Table 104, suppose = 0.10. Which of the following represents the result of the relevant hypothesis test?
 The alternative hypothesis is rejected.
 The null hypothesis is rejected.
 The null hypothesis is not rejected.
 Insufficient information exists on which to make a decision.
 Referring to Table 104, suppose = 0.05. Which of the following represents the result of the relevant hypothesis test?
 The alternative hypothesis is rejected.
 The null hypothesis is rejected.
 The null hypothesis is not rejected.
 Insufficient information exists on which to make a decision.
 Referring to Table 104, suppose = 0.01. Which of the following represents the result of the relevant hypothesis test?
 The alternative hypothesis is rejected.
 The null hypothesis is rejected.
 The null hypothesis is not rejected.
 Insufficient information exists on which to make a decision.
 Referring to Table 104, suppose = 0.1. Which of the following represents the correct conclusion?
 There is not enough evidence that, on average, families in Gotham have been living in their current homes for less time than families in Metropolis have.
 There is enough evidence that, on average, families in Gotham have been living in their current homes for less time than families in Metropolis have.
 There is not enough evidence that, on average, families in Gotham have been living in their current homes for no less time than families in Metropolis have.
 There is enough evidence that, on average, families in Gotham have been living in their current homes for no less time than families in Metropolis have.
 Referring to Table 104, suppose = 0.05. Which of the following represents the correct conclusion?
 There is not enough evidence that, on average, families in Gotham have been living in their current homes for less time than families in Metropolis have.
 There is enough evidence that, on average, families in Gotham have been living in their current homes for less time than families in Metropolis have.
 There is not enough evidence that, on average, families in Gotham have been living in their current homes for no less time than families in Metropolis have.
 There is enough evidence that, on average, families in Gotham have been living in their current homes for no less time than families in Metropolis have.
 Referring to Table 104, suppose = 0.01. Which of the following represents the correct conclusion?
 There is not enough evidence that, on average, families in Gotham have been living in their current homes for less time than families in Metropolis have.
 There is enough evidence that, on average, families in Gotham have been living in their current homes for less time than families in Metropolis have.
 There is not enough evidence that, on average, families in Gotham have been living in their current homes for no less time than families in Metropolis have.
 There is enough evidence that, on average, families in Gotham have been living in their current homes for no less time than families in Metropolis have.
 Referring to Table 104, what is the 99% confidence interval estimate for the difference in the two means?
 Referring to Table 104, what is the 95% confidence interval estimate for the difference in the two means?
TABLE 105
To test the effectiveness of a business school preparation course, 8 students took a general business test before and after the course. The results are given below.
Exam Score Exam Score
Student Before Course (1) After Course (2)
1 530 670
2 690 770
3 910 1,000
4 700 710
5 450 550
6 820 870
7 820 770
8 630 610
 Referring to Table 105, the number of degrees of freedom is
 14.
 13.
 8.
 7.
 Referring to Table 105, the value of the sample mean difference is _______ if the difference scores reflect the results of the exam after the course minus the results of the exam before the course.
 0
 50
 68
 400
 Referring to Table 105, the value of the standard error of the difference scores is
 65.027
 60.828
 22.991
 14.696
 Referring to Table 105, what is the critical value for testing at the 5% level of significance whether the business school preparation course is effective in improving exam scores?
 2.365
 2.145
 1.761
 1.895
 Referring to Table 105, at the 0.05 level of significance, the decision for this hypothesis test would be:
 reject the null hypothesis.
 do not reject the null hypothesis.
 reject the alternative hypothesis.
 It cannot be determined from the information given.
 Referring to Table 105, at the 0.05 level of significance, the conclusion for this hypothesis test would be:
 the business school preparation course does improve exam score.
 the business school preparation course does not improve exam score.
 the business school preparation course has no impact on exam score.
 It cannot be drawn from the information given.
 True or False: Referring to Table 105, one must assume that the population of difference scores is normally distributed.
 Referring to Table 105, the calculated value of the test statistic is ________.
 Referring to Table 105, the pvalue of the test statistic is ________.
 True or False: Referring to Table 105, in examining the differences between related samples we are essentially sampling from an underlying population of difference "scores."
 True or False: The sample size in each independent sample must be the same if we are to test for differences between the means of 2 independent populations.
 True or False: When we test for differences between the means of 2 independent populations, we can only use a twotailed test.
 True or False: When testing for differences between the means of 2 related populations, we can use either a onetailed or twotailed test.
 True or False: Repeated measurements from the same individuals is an example of data collected from 2 related populations.
 True or False: The test for the equality of 2 population variances assumes that each of the 2 populations is normally distributed.
 True or False: For all twosample tests, the sample sizes must be equal in the 2 groups.
 True or False: When the sample sizes are equal, the pooled variance of the 2 groups is the average of the 2 sample variances.
 True or False: The F distribution is symmetric.
 True or False: The F distribution can only have positive values.
 True or False: All F tests are onetailed tests.
 True of False: When performing a twotailed test, the lowertailed critical value of the F distribution with degrees of freedom in the numerator and degrees of freedom in the denominator is exactly equivalent to the reciprocal of the uppertailed critical value of the F distribution with degrees of freedom in the numerator and degrees of freedom in the denominator.
 Given the uppertailed critical value of an F test with 3 degrees of freedom in the numerator and 8 degrees of freedom in the denominator being 4.07, the lowertailed critical value of an F test with 8 degrees of freedom in the numerator and 3 degrees of freedom in the denominator for the same level of significance will be _________.
 True or False: A researcher is curious about the effect of sleep on students’ test performances. He chooses 60 students and gives each 2 tests: one given after 2 hours’ sleep and one after 8 hours’ sleep. The test the researcher should use would be a related samples test.
 When testing , the observed value of the Zscore was found to be – 2.13. The pvalue for this test would be
 0.0166.
 0.0332.
 0.9668.
 0.9834.
 When testing versus , the observed value of the Zscore was found to be – 2.13. The pvalue for this test would be
 0.0166.
 0.0332.
 0.9668.
 0.9834.
 When testing versus , the observed value of the Zscore was found to be – 2.13. The pvalue for this test would be
 0.0166.
 0.0332.
 0.9668.
 0.9834.
 True or False: A statistics professor wanted to test whether the grades on a statistics test were the same for upper and lower classmen. The professor took a random sample of size 10 from each, conducted a test and found out that the variances were equal. For this situation, the professor should use a t test with related samples.
 True or False: A statistics professor wanted to test whether the grades on a statistics test were the same for upper and lower classmen. The professor took a random sample of size 10 from each, conducted a test and found out that the variances were equal. For this situation, the professor should use a t test with independent samples.
 True or False: A Marine drill instructor recorded the time in which each of 11 recruits completed an obstacle course both before and after basic training. To test whether any improvement occurred, the instructor would use a tdistribution with 11 degrees of freedom.
 True or False: A Marine drill instructor recorded the time in which each of 11 recruits completed an obstacle course both before and after basic training. To test whether any improvement occurred, the instructor would use a tdistribution with 10 degrees of freedom.
TABLE 106
Two samples each of size 25 are taken from independent populations assumed to be normally distributed with equal variances. The first sample has a mean of 35.5 and standard deviation of 3.0 while the second sample has a mean of 33.0 and standard deviation of 4.0.
 Referring to Table 106, the pooled (i.e., combined) variance is _______.
 Referring to Table 106, the computed t statistic is _______.
 Referring to Table 106, there are _______ degrees of freedom for this test.
 Referring to Table 106, the critical values for a twotailed test of the null hypothesis of no difference in the population means at the = 0.05 level of significance are _______.
 Referring to Table 106, a twotailed test of the null hypothesis of no difference would _______ (be rejected/not be rejected) at the = 0.05 level of significance.
 Referring to Table 106, the pvalue for a twotailed test whose computed t statistic is 2.50 is between _____ and _______ .
 Referring to Table 106, if we were interested in testing against the onetailed alternative that at the = 0.01 level of significance, the null hypothesis would _______ .
 Referring to Table 106, the pvalue for a onetailed test whose computed statistic is 2.50 (in the hypothesized direction) is between _______ .
 Referring to Table 106, what is the 99% confidence interval estimate for the difference in the two means?
 Referring to Table 106, what is the 95% confidence interval estimate for the difference in the two means?
 Referring to Table 106, what is the 90% confidence interval estimate for the difference in the two means?
TABLE 107
To investigate the efficacy of a diet, a random sample of 16 male patients is drawn from a population of adult males using the diet. The weight of each individual in the sample is taken at the start of the diet and at a medical followup 4 weeks later. Assuming that the population of differences in weight before versus after the diet follow a normal distribution, the ttest for related samples can be used to determine if there was a significant decrease in the mean weight during this period. Suppose the mean decrease in weights over all 16 subjects in the study is 3.0 pounds with the standard deviation of differences computed as 6.0 pounds.
 Referring to Table 107, the t test should be _______tailed.
 Referring to Table 107, the computed t statistic is _______.
 Referring to Table 107, there are _______ degrees of freedom for this test.
 Referring to Table 107, the critical value for a onetailed test of the null hypothesis of no difference at the = 0.05 level of significance is _______.
 Referring to Table 107, a onetailed test of the null hypothesis of no difference would _______ (be rejected/not be rejected) at the = 0.05 level of significance.
 Referring to Table 107, the pvalue for a onetailed test whose computed t statistic is 2.00 is between _______.
 Referring to Table 107, if we were interested in testing against the twotailed alternative that is not equal to zero at the = 0.05 level of significance, the null hypothesis would _______ (be rejected/not be rejected).
 Referring to Table 107, the pvalue for a twotailed test whose computed statistic is 2.00 is between ________ .
 Referring to Table 107, what is the 95% confidence interval estimate for the mean difference in weight before and after the diet?
 Referring to Table 107, what is the 99% confidence interval estimate for the mean difference in weight before and after the diet?
 Referring to Table 107, what is the 90% confidence interval estimate for the mean difference in weight before and after the diet?
TABLE 108
A buyer for a manufacturing plant suspects that his primary supplier of raw materials is overcharging. In order to determine if his suspicion is correct, he contacts a second supplier and asks for the prices on various identical materials. He wants to compare these prices with those of his primary supplier. The data collected is presented in the table below, with some summary statistics presented (all of these might not be necessary to answer the questions which follow). The buyer believes that the differences are normally distributed and will use this sample to perform an appropriate test at a level of significance of 0.01.
Primary Secondary
Material Supplier Supplier Difference
1 $55 $45 $10
2 $48 $47 $1
3 $31 $32 – $1
4 $83 $77 $6
5 $37 $37 $0
6 $55 $54 $1
Sum: $309 $292 $17
Sum of Squares: $17,573 $15,472 $139
 Referring to Table 108, the hypotheses that the buyer should test are a null hypothesis that ________ versus an alternative hypothesis that ________.
 Referring to Table 108, the test to perform is a
 pooledvariance t test for differences between two means.
 separatevariance t test for differences between two means.
 Z test for the difference between two means.
 paired ttest for the mean difference.
 Referring to Table 108, the decision rule is to reject the null hypothesis if ________.
 Referring to Table 108, the calculated value of the test statistic is ________.
 Referring to Table 108, the pvalue of the test is between ________ and ________.
 True or False: Referring to Table 108, the null hypothesis should be rejected.
 Referring to Table 108, the buyer should decide that the primary supplier is
 overcharging because there is strong evidence that this is the case.
 overcharging because there is insufficient evidence to prove otherwise.
 not overcharging because there is insufficient evidence to prove otherwise.
 not overcharging because there is strong evidence to prove otherwise.
 Referring to Table 108, if the buyer had decided to perform a twotailed test, the pvalue would have been between ________ and ________.
 Referring to Table 108, what is the 99% confidence interval estimate for the mean difference in prices?
 Referring to Table 108, what is the 95% confidence interval estimate for the mean difference in prices?
 Referring to Table 108, what is the 90% confidence interval estimate for the mean difference in prices?
 If we wish to determine whether there is evidence that the proportion of successes is higher in group 1 than in group 2, the appropriate test to use is
 the Z test for the difference between two proportions.
 the F test for the difference between two variances.
 the pooledvariance t test for the difference between two proportions.
 the F test for the difference between two proportions.
 Moving companies are required by the government to publish a Carrier Performance Report each year. One of the descriptive statistics they must include is the annual percentage of shipments on which a $50 or greater claim for loss or damage was filed. Suppose two companies, EconoMove and OntheMove, each decide to estimate this figure by sampling their records, and they report the data shown in the following table.

EconoMove

OntheMove

Total shipments sampled

900

750

Number of shipments with a claim $50

162

60

The owner of OntheMove is hoping to use these data to show that the company is superior to EconoMove with regard to the percentage of claims filed. Which test would be used to properly analyze the data in this experiment?
 Z test for the difference between two means
 F test for the difference between two variances
 Separate variance t test for the difference between two means
 Z test for the difference between two proportions
 The Wall Street Journal recently ran an article indicating differences in perception of sexual harassment on the job between men and women. The article claimed that women perceived the problem to be much more prevalent than did men. One question asked of both men and women was: “Do you think sexual harassment is a major problem in the American workplace?” Some 24% of the men compared to 62% of the women responded “Yes.” Assuming W designates women’s responses and M designates men’s, what hypothesis should The Wall Street Journal test in order to show that its claim is true?
 H_{0}: 0 versus H_{1}: < 0
 H_{0}: 0 versus H_{1}: > 0
 H_{0}: = 0 versus H_{1}: 0
 H_{0}: 0 versus H_{1}: > 0
 The Wall Street Journal recently ran an article indicating differences in perception of sexual harassment on the job between men and women. The article claimed that women perceived the problem to be much more prevalent than did men. One question asked to both men and women was: “Do you think sexual harassment is a major problem in the American workplace?” Some 24% of the men compared to 62% of the women responded “Yes.” Suppose that 150 women and 200 men were interviewed. For a 0.01 level of significance, what is the critical value for the rejection region?
 7.173
 7.106
 6.635
 2.33
 The Wall Street Journal recently ran an article indicating differences in perception of sexual harassment on the job between men and women. The article claimed that women perceived the problem to be much more prevalent than did men. One question asked to both men and women was: “Do you think sexual harassment is a major problem in the American workplace?” Some 24% of the men compared to 62% of the women responded “Yes.” Suppose that 150 women and 200 men were interviewed. What is the value of the test statistic?
 7.173
 7.106
 6.635
 2.33
 The Wall Street Journal recently ran an article indicating differences in perception of sexual harassment on the job between men and women. The article claimed that women perceived the problem to be much more prevalent than did men. One question asked to both men and women was: “Do you think sexual harassment is a major problem in the American workplace?” Some 24% of the men compared to 62% of the women responded “Yes.” Suppose that 150 women and 200 men were interviewed. Construct a 99% confidence interval estimate of the difference between the proportion of women and men who think sexual harassment is a major problem in the American workplace.
 The Wall Street Journal recently ran an article indicating differences in perception of sexual harassment on the job between men and women. The article claimed that women perceived the problem to be much more prevalent than did men. One question asked to both men and women was: “Do you think sexual harassment is a major problem in the American workplace?” Some 24% of the men compared to 62% of the women responded “Yes.” Suppose that 150 women and 200 men were interviewed. Construct a 95% confidence interval estimate of the difference between the proportion of women and men who think sexual harassment is a major problem in the American workplace.
 The Wall Street Journal recently ran an article indicating differences in perception of sexual harassment on the job between men and women. The article claimed that women perceived the problem to be much more prevalent than did men. One question asked to both men and women was: “Do you think sexual harassment is a major problem in the American workplace?” Some 24% of the men compared to 62% of the women responded “Yes.” Suppose that 150 women and 200 men were interviewed. Construct a 90% confidence interval estimate of the difference between the proportion of women and men who think sexual harassment is a major problem in the American workplace.
 The Wall Street Journal recently ran an article indicating differences in perception of sexual harassment on the job between men and women. The article claimed that women perceived the problem to be much more prevalent than did men. One question asked to both men and women was: “Do you think sexual harassment is a major problem in the American workplace?” Some 24% of the men compared to 62% of the women responded “Yes.” Suppose that 150 women and 200 men were interviewed. What conclusion should be reached?
 Using a 0.01 level of significance, there is sufficient evidence to conclude that women perceive the problem of sexual harassment on the job as much more prevalent than do men.
 There is insufficient evidence to conclude with at least 99% confidence that women perceive the problem of sexual harassment on the job as much more prevalent than do men.
 There is no evidence of a significant difference between the men and women in their perception.
 More information is needed to draw any conclusions from the data set.
 A powerful women’s group has claimed that men and women differ in attitudes about sexual discrimination. A group of 50 men (group 1) and 40 women (group 2) were asked if they thought sexual discrimination is a problem in the United States. Of those sampled, 11 of the men and 19 of the women did believe that sexual discrimination is a problem. Assuming W designates women’s responses and M designates men’s, which of the following are the appropriate null and alternative hypotheses to test the group’s claim?
 H_{0}: 0 versus H_{1}: < 0
 H_{0}: 0 versus H_{1}: > 0
 H_{0}: = 0 versus H_{1}: 0
 H_{0}: 0 versus H_{1}: = 0
 A powerful women’s group has claimed that men and women differ in attitudes about sexual discrimination. A group of 50 men (group 1) and 40 women (group 2) were asked if they thought sexual discrimination is a problem in the United States. Of those sampled, 11 of the men and 19 of the women did believe that sexual discrimination is a problem. Find the value of the test statistic.
 Z = – 2.55
 Z = – 0.85
 Z = – 1.05
 Z = – 1.20
 A powerful women’s group has claimed that men and women differ in attitudes about sexual discrimination. A group of 50 men (group 1) and 40 women (group 2) were asked if they thought sexual discrimination is a problem in the United States. Of those sampled, 11 of the men and 19 of the women did believe that sexual discrimination is a problem. If the pvalue turns out to be 0.035 (which is not the real value in this data set), then
 at = 0.05, we should fail to reject H_{0}
 at = 0.04, we should reject H_{0}
 at = 0.03, we should reject H_{0}
 None of the above would be correct statements.
 A powerful women’s group has claimed that men and women differ in attitudes about sexual discrimination. A group of 50 men (group 1) and 40 women (group 2) were asked if they thought sexual discrimination is a problem in the United States. Of those sampled, 11 of the men and 19 of the women did believe that sexual discrimination is a problem. Construct a 99% confidence interval estimate of the difference between the proportion of men and women who believe that sexual discrimination is a problem.
 A powerful women’s group has claimed that men and women differ in attitudes about sexual discrimination. A group of 50 men (group 1) and 40 women (group 2) were asked if they thought sexual discrimination is a problem in the United States. Of those sampled, 11 of the men and 19 of the women did believe that sexual discrimination is a problem. Construct a 95% confidence interval estimate of the difference between the proportion of men and women who believe that sexual discrimination is a problem.
 A powerful women’s group has claimed that men and women differ in attitudes about sexual discrimination. A group of 50 men (group 1) and 40 women (group 2) were asked if they thought sexual discrimination is a problem in the United States. Of those sampled, 11 of the men and 19 of the women did believe that sexual discrimination is a problem. Construct a 90% confidence interval estimate of the difference between the proportion of men and women who believe that sexual discrimination is a problem.
TABLE 109
A few years ago, Pepsi invited consumers to take the “Pepsi Challenge.” Consumers were asked to decide which of two sodas, Coke or Pepsi, they preferred in a blind taste test. Pepsi was interesting in determining what factors played a role in people’s taste preferences. One of the factors studied was the gender of the consumer. Below are the results of analyses comparing the taste preferences of men and women with the proportions depicting preference for Pepsi.
Males: n = 109, p_{M} = 0.422018 Females: n = 52, p_{F} = 0.25
p_{M} – p_{F} = 0.172018 Z = 2.11825
 Referring to Table 109, to determine if a difference exists in the taste preferences of men and women, give the correct alternative hypothesis that Pepsi would test.
 H_{1}:
 H_{1}:
 H_{1}: 0
 H_{1}: = 0
 Referring to Table 109, suppose Pepsi wanted to test to determine if the males preferred Pepsi more than the females. Using the test statistic given, compute the appropriate pvalue for the test.
 0.0171
 0.0340
 0.2119
 0.4681
 Referring to Table 109, suppose Pepsi wanted to test to determine if the males preferred Pepsi less than the females. Using the test statistic given, compute the appropriate pvalue for the test.
 0.0170
 0.0340
 0.9660
 0.9830
 Referring to Table 109, suppose that the twotailed pvalue was really 0.0734. State the proper conclusion.
 At = 0.05, there is sufficient evidence to indicate the proportion of males preferring Pepsi differs from the proportion of females preferring Pepsi.
 At = 0.10, there is sufficient evidence to indicate the proportion of males preferring Pepsi differs from the proportion of females preferring Pepsi.
 At = 0.05, there is sufficient evidence to indicate the proportion of males preferring Pepsi equals the proportion of females preferring Pepsi.
 At = 0.08, there is insufficient evidence to indicate the proportion of males preferring Pepsi differs from the proportion of females preferring Pepsi.
 Referring to Table 109, construct a 90% confidence interval estimate of the difference between the proportion of males and females who prefer Pepsi.
 Referring to Table 109, construct a 95% confidence interval estimate of the difference between the proportion of males and females who prefer Pepsi.
 Referring to Table 109, construct a 99% confidence interval estimate of the difference between the proportion of males and females who prefer Pepsi.
TABLE 1010
The following EXCEL output contains the results of a test to determine if the proportions of satisfied guests at two resorts are the same or different.
Hypothesized Difference

0

Level of Significance

0.05

Group 1

Number of Successes

163

Sample Size

227

Group 2

Number of Successes

154

Sample Size

262

Group 1 Proportion

0.718061674

Group 2 Proportion

0.58778626

Difference in Two Proportions

0.130275414

Average Proportion

0.648261759

Test Statistic

3.00875353

TwoTailed Test

Lower Critical Value

?1.959961082

Upper Critical Value

1.959961082

pValue

0.002623357

 Referring to Table 1010, allowing for 0.75% probability of committing a Type I error, what are the decision and conclusion on testing whether there is any difference in the proportions of satisfied guests in the two resorts?
 Do not reject the null hypothesis; there is enough evidence to conclude that there is significant difference in the proportions of satisfied guests at the two resorts.
 Do not reject the null hypothesis; there is not enough evidence to conclude that there is significant difference in the proportions of satisfied guests at the two resorts.
 Reject the null hypothesis; there is enough evidence to conclude that there is significant difference in the proportions of satisfied guests at the two resorts.
 Reject the null hypothesis; there is not enough evidence to conclude that there is significant difference in the proportions of satisfied guests at the two resorts.
 Referring to Table 1010, if you want to test the claim that "Resort 1 (Group 1) has a higher proportion of satisfied guests compared to Resort 2 (Group 2)", the pvalue of the test will be
 0.00262
 0.00262/2
 2(0.00262)
 1(0.00262/2)
 Referring to Table 1010, if you want to test the claim that "Resort 1 (Group 1) has a lower proportion of satisfied guests compared to Resort 2 (Group 2)", you will use
 a ttest for the difference between two proportions.
 a ztest for the difference between two proportions.
 an F test for the difference between two proportions.
 a test for the difference between two proportions.
 Referring to Table 1010, construct a 99% confidence interval estimate of the difference in the population proportion of satisfied guests between the two resorts.
 Referring to Table 1010, construct a 95% confidence interval estimate of the difference in the population proportion of satisfied guests between the two resorts.
 Referring to Table 1010, construct a 90% confidence interval estimate of the difference in the population proportion of satisfied guests between the two resorts.
TABLE 1011
A corporation randomly selects 150 salespeople and finds that 66% who have never taken a selfimprovement course would like such a course. The firm did a similar study 10 years ago in which 60% of a random sample of 160 salespeople wanted a selfimprovement course. The groups are assumed to be independent random samples. Let and represent the true proportion of workers who would like to attend a selfimprovement course in the recent study and the past study, respectively.
 Referring to Table 1011, if the firm wanted to test whether this proportion has changed from the previous study, which represents the relevant hypotheses?
 H_{0}: = 0 versus H_{1}: 0
 H_{0}: 0 versus H_{1}: = 0
 H_{0}: 0 versus H_{1}: > 0
 H_{0}: 0 versus H_{1}: < 0
 Referring to Table 1011, if the firm wanted to test whether a greater proportion of workers would currently like to attend a selfimprovement course than in the past, which represents the relevant hypotheses?
 H_{0}: = 0 versus H_{1}: 0
 H_{0}: 0 versus H_{1}: = 0
 H_{0}: 0 versus H_{1}: > 0
 H_{0}: 0 versus H_{1}: < 0
 Referring to Table 1011, what is the unbiased point estimate for the difference between the two population proportions?
 0.06
 0.10
 0.15
 0.22
 Referring to Table 1011, what is/are the critical value(s) when performing a Z test on whether population proportions are different if = 0.05?
 1.645
 1.96
 ?1.96
 2.08
 Referring to Table 1011, what is/are the critical value(s) when testing whether population proportions are different if = 0.10?
 1.645
 1.96
 1.96
 2.08
 Referring to Table 1011, what is/are the critical value(s) when testing whether the current population proportion is higher than before if = 0.05?
 1.645
 + 1.645
 1.96
 + 1.96
 Referring to Table 1011, what is the estimated standard error of the difference between the two sample proportions?
 0.629
 0.500
 0.055
 0
 Referring to Table 1011, what is the value of the test statistic to use in evaluating the alternative hypothesis that there is a difference in the two population proportions?
 4.335
 1.96
 1.093
 0
 Referring to Table 1011, the company tests to determine at the 0.05 level whether the population proportion has changed from the previous study. Which of the following is most correct?
 Reject the null hypothesis and conclude that the proportion of employees who are interested in a selfimprovement course has changed over the intervening 10 years.
 Do not reject the null hypothesis and conclude that the proportion of employees who are interested in a selfimprovement course has not changed over the intervening 10 years.
 Reject the null hypothesis and conclude that the proportion of employees who are interested in a selfimprovement course has increased over the intervening 10 years.
 Do not reject the null hypothesis and conclude that the proportion of employees who are interested in a selfimprovement course has increased over the intervening 10 years.
 Referring to Table 1011, construct a 99% confidence interval estimate of the difference in proportion of workers who would like to attend a selfimprovement course in the recent study and the past study.
 Referring to Table 1011, construct a 95% confidence interval estimate of the difference in proportion of workers who would like to attend a selfimprovement course in the recent study and the past study.
 Referring to Table 1011, construct a 90% confidence interval estimate of the difference in proportion of workers who would like to attend a selfimprovement course in the recent study and the past study.
 True or False: In testing the difference between two proportions using the normal distribution, we may use a twotailed Z test.
 If we wish to determine whether there is evidence that the proportion of successes is higher in Group 1 than in Group 2, and the test statistic for Z = +2.07 where the difference is defined as Group 1’s proportion minus Group 2’s proportion, the pvalue is equal to ______.
 If we wish to determine whether there is evidence that the proportion of successes is higher in Group 1 than in Group 2, and the test statistic for Z = ?2.07 where the difference is defined as Group 1’s proportion minus Group 2’s proportion, the pvalue is equal to ______.
TABLE 1012
The dean of a college is interested in the proportion of graduates from his college who have a job offer on graduation day. He is particularly interested in seeing if there is a difference in this proportion for accounting and economics majors. In a random sample of 100 of each type of major at graduation, he found that 65 accounting majors and 52 economics majors had job offers. If the accounting majors are designated as “Group 1” and the economics majors are designated as “Group 2,” perform the appropriate hypothesis test using a level of significance of 0.05.
 Referring to Table 1012, the hypotheses the dean should use are:
 H_{0}: = 0 versus H_{1}: 0
 H_{0}: 0 versus H_{1}: = 0
 H_{0}: 0 versus H_{1}: > 0
 H_{0}: 0 versus H_{1}: < 0
 Referring to Table 1012, the null hypothesis will be rejected if the test statistic is ________.
 Referring to Table 1012, the value of the test statistic is ________.
 Referring to Table 1012, the pvalue of the test is ________.
 True or False: Referring to Table 1012, the null hypothesis should be rejected.
 True or False: Referring to Table 1012, the same decision would be made with this test if the level of significance had been 0.01 rather than 0.05.
 True or False: Referring to Table 1012, the same decision would be made with this test if the level of significance had been 0.10 rather than 0.05.
 Referring to Table 1012, construct a 99% confidence interval estimate of the difference in proportion between accounting majors and economic majors who have a job offer on graduation day.
 Referring to Table 1012, construct a 95% confidence interval estimate of the difference in proportion between accounting majors and economic majors who have a job offer on graduation day.
 Referring to Table 1012, construct a 90% confidence interval estimate of the difference in proportion between accounting majors and economic majors who have a job offer on graduation day.
TABLE 1013
A quality control engineer is in charge of the manufacture of computer disks. Two different processes can be used to manufacture the disks. He suspects that the Kohler method produces a greater proportion of defects than the Russell method. He samples 150 of the Kohler and 200 of the Russell disks and finds that 27 and 18 of them, respectively, are defective. If Kohler is designated as “Group 1” and Russell is designated as “Group 2,” perform the appropriate test at a level of significance of 0.01.
 Referring to Table 1013, the hypotheses that should be tested are:
 H_{0}: = 0 versus H_{1}: 0
 H_{0}: 0 versus H_{1}: = 0
 H_{0}: 0 versus H_{1}: > 0
 H_{0}: 0 versus H_{1}: < 0
 Referring to Table 1013, the null hypothesis will be rejected if the test statistic is ________.
 Referring to Table 1013, the value of the test statistic is ________.
 Referring to Table 1013, the pvalue of the test is ________.
 True or False: Referring to Table 1013, the null hypothesis should be rejected.
 True or False: Referring to Table 1013, the same decision would be made with this test if the level of significance had been 0.05 rather than 0.01.
 True or False: Referring to Table 1013, the same decision would be made if this had been a twotailed test at a level of significance of 0.01.
 Referring to Table 1013, construct a 90% confidence interval estimate of the difference in proportion between the Kohler and Russell disks that are defective.
 Referring to Table 1013, construct a 95% confidence interval estimate of the difference in proportion between the Kohler and Russell disks that are defective.
 Referring to Table 1013, construct a 99% confidence interval estimate of the difference in proportion between the Kohler and Russell disks that are defective.