Exam 10: Two-Sample Tests

SCENARIO 10-8 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 interested 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,=0.422018 Females: n=52,=0.25 -=0.172018Z=2.11825 -Referring to Scenario 10-8, construct a 99% confidence interval estimate of the difference between the proportion of males and females who prefer Pepsi.

SCENARIO 10-1 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 Sample Mean SSATL Score 65.75 79.83 Sample Std. Dev. 11.07 6.41 -Referring to Scenario 10-1, judging from the way the data were collected, which test would likely be most appropriate to employ?

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?

SCENARIO 10-16-B 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-DataB.XLSX. Men 122 184 220 61 114 293 107 200 242 233 229 157 203 147 110 217 136 222 206 155 292 220 210 196 177 212 169 243 240 78 226 173 152 228 230 162 189 171 184 263 217 170 191 176 129 241 208 217 251 267 Women 170 180 167 232 217 145 190 145 200 163 159 138 193 170 165 172 190 127 186 245 198 186 163 129 158 164 197 182 172 163 180 168 158 185 166 216 153 146 197 129 162 202 192 119 197 172 139 167 203 130 Treat the men as population 1 and the women as population 2. -Referring to Scenario 10-16-B, 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 assumption(s) is(are) necessary when testing whether there is evidence of a difference in the variances to be valid?

Given the following information, calculate the degrees of freedom that should be used in the pooled-variance t test. =4 =6 =16 =25 a) $d f = 41$ b) $d f = 39$ c) $d f = 16$ d) $d f = 25$

The Wall Street Journal recently published 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?" 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? a) $H _ { 0 } : \pi _ { W } - \pi _ { M } \geq 0$ versus $H _ { 1 } : \pi _ { W } - \pi _ { M } < 0$ b) $H _ { 0 } : \pi _ { W } - \pi _ { M } \leq 0$ versus $H _ { 1 } : \pi _ { W } - \pi _ { M } > 0$ c) $H _ { 0 } : \pi _ { W } - \pi _ { M } = 0$ versus $H _ { 1 } : \pi _ { W } - \pi _ { M } \neq 0$ d) $H _ { 0 } : \pi _ { W } - \pi _ { M } \neq 0$ versus $H _ { 1 } : \pi _ { W } - \pi _ { M } = 0$

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(are) the critical value(s) 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 10-1 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 Sample Mean SSATL Score 65.75 79.83 Sample Std. Dev. 11.07 6.41 -Referring to Scenario 10-1, what is the value of the test statistic?

SCENARIO 10-4 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 Scenario 10-6, the pooled (i.e., combined) variance is _______.

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, the researcher was attempting to show statistically that the female MBA graduates have a significantly lower mean starting salary than the male MBA graduates. Which of the following is an appropriate alternative hypothesis? a) $H _ { 1 } : \mu _ { \text {females } } > \mu _ { \text {males } }$ b) $H _ { 1 } : \mu _ { \text {females } } < \mu _ { \text {males } }$ c) $H _ { 1 } : \mu _ { \text {females } } \neq \mu _ { \text {males } }$ d) $H _ { 1 } : \mu _ { \text {females } } = \mu _ { \text {males } }$

SCENARIO 10-13 The amount of time required to reach a customer service representative has a huge impact on customer satisfaction. Below is the Excel output from a study to see whether there is evidence of a difference in the mean amounts of time required to reach a customer service representative between two hotels. Assume that the population variances in the amount of time for the two hotels are not equal. t-Test: Two-Sample Assuming Unequal Variances Hotel 1 Hotel 2 Mean 2.214 2.0115 Variance 2.951657 3.57855 Observations 20 20 Hypothesized Mean Difference 0 df 38 t Stat 0.354386 P(T<=t) one-tail 0.362504 Critical one-tail 1.685953 (<=) two-tail 0.725009 Critical two-tail 2.024394 -Referring to Scenario 10-13, suppose ? = 0.05. Which of the following represents the correct conclusion for a test on a difference in the variabilities of the amount of time required to reach a Customer service representative between the two hotels?

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, 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?

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 are the null and alternative hypotheses when testing whether there is evidence of a difference in the means of monthly online shopping spending between men and women?

SCENARIO 10-13 The amount of time required to reach a customer service representative has a huge impact on customer satisfaction. Below is the Excel output from a study to see whether there is evidence of a difference in the mean amounts of time required to reach a customer service representative between two hotels. Assume that the population variances in the amount of time for the two hotels are not equal. t-Test: Two-Sample Assuming Unequal Variances Hotel 1 Hotel 2 Mean 2.214 2.0115 Variance 2.951657 3.57855 Observations 20 20 Hypothesized Mean Difference 0 df 38 t Stat 0.354386 P(T<=t) one-tail 0.362504 Critical one-tail 1.685953 (<=) two-tail 0.725009 Critical two-tail 2.024394 -Referring to Scenario 10-13, suppose ? = 0.10. Which of the following represents the correct conclusion?

When testing for the difference between 2 population variances with sample sizes of n1 = 8 and n2 = 10, where n1 has the larger variance, the number of degrees of freedom are

SCENARIO 10-9 The following EXCEL output contains the results of a test to determine whether the proportions of satisfied customers at two resorts are the same or different. -Referring to Scenario 10-9, if you want to test the claim that "Resort 1 (Group 1) has a higher proportion of satisfied customers compared to Resort 2 (Group 2)", the p-value of the test will be

SCENARIO 10-6 To investigate the efficacy of a diet, a random sample of 16 male patients is selected 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 follow-up 4 weeks later. Assuming that the population of differences in weight before versus after the diet follow a normal distribution, the t-test 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 Scenario 10-6, the p-value for a one-tail test is _______.

SCENARIO 10-1 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 Sample Mean SSATL Score 65.75 79.83 Sample Std. Dev. 11.07 6.41 -Referring to Scenario 10-1, give the null and alternative hypotheses to determine if the mean SSATL score of Japanese managers differs from the mean SSATL score of American managers. a) $H _ { 0 } : \mu _ { A } - \mu _ { J } \geq 0$ versus $H _ { 1 } : \mu _ { A } - \mu _ { J } < 0$ b) $H _ { 0 } : \mu _ { A } - \mu _ { J } \leq 0$ versus $H _ { 1 } : \mu _ { A } - \mu _ { J } > 0$ c) $H _ { 0 } : \mu _ { A } - \mu _ { J } = 0$ versus $H _ { 1 } : \mu _ { A } - \mu _ { J } \neq 0$ d) $H _ { 0 } : \bar { X } _ { A } - \bar { X } _ { J } = 0$ versus $H _ { 1 } : \bar { X } _ { A } - \bar { X } _ { J } \neq 0$

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 99% confidence interval estimate for the difference between two means?