Exam 10: Two-Sample Tests

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

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 95% confidence interval estimate for the difference in the two means?

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, construct a 99% confidence interval estimate of the difference in proportion between the Kohler and Russell flash drives that are defective.

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 ? = 0.01. Which of the following represents the result of the relevant hypothesis test?

The statistical distribution used for testing the difference between two population variances is the ___ distribution.

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 highest level of significance at which a test on a difference in the variances will not be rejected?

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, suppose α = 0.05. What should be your conclusion on 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 variances?

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, the normality probability plot suggests that monthly online shopping spending for the men is quite normally distributed.

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, the p-value for a two-tail test 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. What assumptions were necessary to conduct this hypothesis test?

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, there are _______ degrees of freedom for this test.

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 for testing whether there is evidence of a difference in the variances?

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, if yμ1 > μ2 at the α = 0.01 level of significance, the null hyou were interested in testing against the one-tail alternative that pothesis would ______ (be rejected/not be rejected).

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 ? = 0.01. Which of the following represents the correct conclusion?

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 90% confidence interval estimate of the difference between the proportion of males and females who prefer Pepsi.

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 critical value 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 at the 5% level of significance?

In testing for differences between the means of 2 related populations where the variance of the differences is unknown, the degrees of freedom are a) $n - 1$ . b) $n _ { 1 } + n _ { 2 } - 1$ . c) $n _ { 1 } + n _ { 2 } - 2$ . d) $n - 2$ .

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 90% confidence interval estimate of the difference in the population proportion of satisfied customers between the two resorts.

In testing for the differences between the means of two related populations, you assume that the differences follow a _______ distribution.

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 90% confidence interval estimate for the mean difference in prices?