Exam 10: Two-Sample Tests

The t test for the mean difference between 2 related populations assumes that the

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 90% confidence interval estimate for the difference between two means?

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, what assumption(s) is(are) necessary when testing whether there is evidence of a difference in the variances to be valid?

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, allowing for 1% 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 customers in the two resorts?

SCENARIO 10-12 A quality control engineer is in charge of the manufacture of USB flash drives. Two different processes can be used to manufacture the flash drives. 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 flash drives 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 Scenario 10-12, the same decision would be made if this had been a two-tail test at a level of significance of 0.01.

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, construct a 95% confidence interval estimate of the difference in the population proportion of satisfied guests between the two resorts.

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, what is the point estimate for the difference between the two population proportions?

The test for the equality of two population variances is based on

The t test for the difference between the means of 2 independent populations assumes that the respective

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 10-4, what is the 90% confidence interval estimate for the difference in the two means?

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 p-value of the test statistic is ________.

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 smallest level of significance at which the null hypothesis will still not be rejected when testing whether there is evidence of a difference in the means of monthly online shopping spending between men and women based on the conclusion that you have reached in testing for evidence of a difference in the?

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.

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.

In testing for differences between the means of two independent populations, the null hypothesis is: a) $H _ { 0 } : \mu _ { 1 } - \mu _ { 2 } = 2$ . b) $H _ { 0 } : \mu _ { 1 } - \mu _ { 2 } = 0$ . c) $H _ { 0 } : \mu _ { 1 } - \mu _ { 2 } > 0$ . d) $H _ { 0 } : \mu _ { 1 } - \mu _ { 2 } < 2$ .

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, what is the value of the test statistic?

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

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, find the p-value if we assume that the alternative hypothesis was a two-tail test.

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 variances 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, what assumptions are necessary for testing if there is evidence of a difference in the variabilities of the amount of time required to reach a customer service Representative between the two hotels to be valid?