Exam 10: Two-Sample Tests

SCENARIO 10-16-A A survey on men and women's shopping behavior collected data from a sample of 50 men and 50 women. The following data on online shopping spending every month are stored in the file Scenario10-16-DataA.XLSX. Men 148 211 256 309 190 205 203 208 231 125 149 205 195 178 196 198 110 199 181 168 218 222 206 168 239 130 246 149 262 142 174 181 198 147 143 185 200 166 171 133 Women 295 242 299 209 189 173 109 291 208 227 272 176 251 235 145 179 30 135 200 270 174 123 199 195 192 102 110 184 228 316 170 234 163 245 174 126 227 86 96 185 288 154 217 184 154 217 222 175 265 196 172 113 240 235 269 243 131 134 56 164 Treat the men as population 1 and the women as population 2. -Referring to Scenario 10-16-A, generate the normal probability plot for the monthly online shopping spending for the women.

SCENARIO 10-16-A A survey on men and women's shopping behavior collected data from a sample of 50 men and 50 women. The following data on online shopping spending every month are stored in the file Scenario10-16-DataA.XLSX. Men 148 211 256 309 190 205 203 208 231 125 149 205 195 178 196 198 110 199 181 168 218 222 206 168 239 130 246 149 262 142 174 181 198 147 143 185 200 166 171 133 Women 295 242 299 209 189 173 109 291 208 227 272 176 251 235 145 179 30 135 200 270 174 123 199 195 192 102 110 184 228 316 170 234 163 245 174 126 227 86 96 185 288 154 217 184 154 217 222 175 265 196 172 113 240 235 269 243 131 134 56 164 Treat the men as population 1 and the women as population 2. -Referring to Scenario 10-16-A, what is the critical value when testing whether there is evidence of a difference in the variances at the 5% level of significance?

SCENARIO 10-5 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. Student Exam Score Before Course (1) Exam Score 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 Scenario 10-5, the value of the standard error of the difference scores is

SCENARIO 10-5 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. Student Exam Score Before Course (1) Exam Score 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 Scenario 10-5, you must assume that the population of difference scores is normally distributed.

SCENARIO 10-5 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. Student Exam Score Before Course (1) Exam Score 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 Scenario 10-5, the p-value of the test statistic is ________.

SCENARIO 10-14 The use of preservatives by food processors has become a controversial issue. Suppose two 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 I and 15 are treated with preservative II, 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 I Preservative II Preservative I Preservative II =106.4 hours =96.54 hours =10.3 hours =13.4 hours -Referring to Scenario 10-14, what is the value of the test statistic for testing if the population variances differ for preservatives I and II?

SCENARIO 10-15 The table below presents the summary statistics for the starting annual salaries (in thousands of dollars) for individuals entering the public accounting and financial planning professions. Sample I (public accounting): $\bar { X } _ { 1 } = 60.35 , S _ { 1 } = 3.25 , n _ { 1 } = 12$ Sample II (financial planning): $\bar { X } _ { 2 } = 58.20 , S _ { 2 } = 2.48 , n _ { 2 } = 14$ Test whether the mean starting annual salaries for individuals entering the public accounting professions is higher than that of financial planning assuming that the two population variances are the same. -Referring to Scenario 10-15, what is the value of the test statistic?

SCENARIO 10-2 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. The result of the pooled-variance t-test of the mean salaries of the females (Population 1) and males (Population 2) in the sample is given below. -Referring to Scenario 10-2, what is the 95% confidence interval estimate for the difference between two means?

SCENARIO 10-16-A A survey on men and women's shopping behavior collected data from a sample of 50 men and 50 women. The following data on online shopping spending every month are stored in the file Scenario10-16-DataA.XLSX. Men 148 211 256 309 190 205 203 208 231 125 149 205 195 178 196 198 110 199 181 168 218 222 206 168 239 130 246 149 262 142 174 181 198 147 143 185 200 166 171 133 Women 295 242 299 209 189 173 109 291 208 227 272 176 251 235 145 179 30 135 200 270 174 123 199 195 192 102 110 184 228 316 170 234 163 245 174 126 227 86 96 185 288 154 217 184 154 217 222 175 265 196 172 113 240 235 269 243 131 134 56 164 Treat the men as population 1 and the women as population 2. -Referring to Scenario 10-16-A, what is the value of the test statistic when testing whether there is evidence of a difference in the means of monthly online shopping spending between men and women if the level of significance is 0.05 based on the conclusion that you have reached in testing for evidence of a difference in the variances?

SCENARIO 10-7 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. -Referring to Scenario 10-7, what is the 95% confidence interval estimate for the mean difference in prices?

When you test for differences between the means of two independent populations, you can only use a two-tail test.

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 t-distribution with 10 degrees of freedom.

F tests are one-tail tests.

SCENARIO 10-3 A real estate company is interested in testing whether the mean time that families in Gotham have been living in their current homes is less than families in Metropolis. 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: $\bar { X } _ { \mathrm { G } } = 35 \text { months, } \quad S _ { \mathrm { G } } { } ^ { 2 } = 900 \quad \text { Metropolis: } \quad \bar { X } _ { \mathrm { M } } = 50 \text { months, } \quad S _ { \mathrm { M } } ^ { 2 } = 1050$ -Referring to Scenario 10-3, what is the 95% confidence interval estimate for the difference in the two means?

SCENARIO 10-10 A corporation randomly selects 150 salespeople and finds that 66% who have never taken a self- improvement 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 self-improvement course. The groups are assumed to be independent random samples. Let $\pi _ { 1 } \text { and } \pi _ { 2 }$ represent the true proportion of workers who would like to attend a self-improvement course in the recent study and the past study, respectively. -Referring to Scenario 10-10, construct a 99% confidence interval estimate of the difference in proportion of workers who would like to attend a self-improvement course in the recent study and the past study.

SCENARIO 10-15 The table below presents the summary statistics for the starting annual salaries (in thousands of dollars) for individuals entering the public accounting and financial planning professions. Sample I (public accounting): $\bar { X } _ { 1 } = 60.35 , S _ { 1 } = 3.25 , n _ { 1 } = 12$ Sample II (financial planning): $\bar { X } _ { 2 } = 58.20 , S _ { 2 } = 2.48 , n _ { 2 } = 14$ Test whether the mean starting annual salaries for individuals entering the public accounting professions is higher than that of financial planning assuming that the two population variances are the same. -Referring to Scenario 10-15, suppose ? = 0.05. Which of the following represents the correct conclusion for a test on a difference in the variances?

SCENARIO 10-7 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. -Referring to Scenario 10-7, the null hypothesis should be rejected.

For all two-sample tests, the sample sizes must be equal in the two groups.

SCENARIO 10-15 The table below presents the summary statistics for the starting annual salaries (in thousands of dollars) for individuals entering the public accounting and financial planning professions. Sample I (public accounting): $\bar { X } _ { 1 } = 60.35 , S _ { 1 } = 3.25 , n _ { 1 } = 12$ Sample II (financial planning): $\bar { X } _ { 2 } = 58.20 , S _ { 2 } = 2.48 , n _ { 2 } = 14$ Test whether the mean starting annual salaries for individuals entering the public accounting professions is higher than that of financial planning assuming that the two population variances are the same. -Referring to Scenario 10-15, state the null and alternative hypotheses for testing whether there is evidence of a difference in the variances of the starting annual salaries. a) $H _ { 0 } : \sigma _ { 1 } ^ { 2 } - \sigma _ { 2 } ^ { 2 } \geq 0$ versus $H _ { 1 } : \sigma _ { 1 } ^ { 2 } - \sigma _ { 2 } ^ { 2 } < 0$ b) $H _ { 0 } : \sigma _ { 1 } ^ { 2 } - \sigma _ { 2 } ^ { 2 } \leq 0$ versus $H _ { 1 } : \sigma _ { 1 } ^ { 2 } - \sigma _ { 2 } ^ { 2 } > 0$ c) $H _ { 0 } : \sigma _ { 1 } ^ { 2 } - \sigma _ { 2 } ^ { 2 } = 0$ versus $H _ { 1 } : \sigma _ { 1 } ^ { 2 } - \sigma _ { 2 } ^ { 2 } \neq 0$ d) $H _ { 0 } : \sigma _ { 1 } ^ { 2 } - \sigma _ { 2 } ^ { 2 } \neq 0$ versus $H _ { 1 } : \sigma _ { 1 } ^ { 2 } - \sigma _ { 2 } ^ { 2 } = 0$

SCENARIO 10-11 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 Scenario 10-11, 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.