Question

Bank A and Bank B have each developed an improved process for serving customers. The waiting period from the moment a customer enters until he or she reaches the counter needs to be shortened. A random sample of 10 customers is selected from each bank and the results​ (in minutes) are shown in the accompanying data table. Complete parts​ (a) through ​(d)

Bank A   Bank B
2.92   3.86
2.84   4.17
3.22   4.94
3.45   5.54
3.64   5.02
4.98   6.31
4.58   6.37
4.54   7.35
5.63   8.18
5.32   10.54

a. Assuming that the population variances from both banks are​ equal, is there evidence of a difference in the mean waiting time between the two​ branches? (Use alpha equals 0.1 .​) Determine the hypotheses. Let mu 1 be the mean waiting time of bank A and mu 2 be the waiting time of bank B.Choose the correct answer below. A. Upper H 0​: mu 1 equals mu 2 Upper H 1​: mu 1 not equals mu 2 B. Upper H 0​: mu 1 not equals mu 2 Upper H 1​: mu 1 equals mu 2 C. Upper H 0​: mu 1 less than or equals mu 2 Upper H 1​: mu 1 greater than mu 2 D. Upper H 0​: mu 1 greater than or equals mu 2 Upper H 1​: mu 1 less than mu 2 Find the test statistic. t Subscript STATequals nothing ​(Round to two decimal places as​ needed.) Find the critical​ value(s). nothing ​(Use a comma to separate answers as needed. Round to three decimal places as​ needed.) Choose the correct conclusion below. A. Reject Upper H 0. There is insufficient evidence that the mean waiting time between the two branches differ. B. Reject Upper H 0. There is sufficient evidence that the mean waiting time between the two branches differ. C. Do not reject Upper H 0. There is insufficient evidence that the mean waiting time between the two branches differ. D. Do not reject Upper H 0. There is sufficient evidence that the mean waiting time between the two branches differ.

b. Determine the​ p-value in​ (a) and interpret its meaning. ​p-valueequals nothing ​(Round to four decimal places as​ needed.) Interpret the​ p-value. Choose the correct answer below. A. It is the probability of obtaining a sample that yields a t test statistic farther away from 0 in either direction than the computed test statistic if there is no difference in the mean waiting time between Bank A and Bank B. B. It is the probability of obtaining a sample that yields a t test statistic farther away from 0 in the positive direction than the computed test statistic if there is no difference in the mean waiting time between Bank A and Bank B. C. It is the probability of obtaining a sample that yields a t test statistic farther away from 0 in the negative direction than the computed test statistic if there is no difference in the mean waiting time between Bank A and Bank B.

c. In addition to equal​ variances, what other assumption is necessary in​ (a)? A. Both sampled populations are not approximately normal. B. The sample sizes must be equal. C. The samples are specifially chosen and not independently sampled. D. Both sampled populations are approximately normal.

d. Construct and interpret a 90​% confidence interval estimate of the difference between the population means between bank A and bank B. The confidence interval is nothingless than or equalsmu 1 minus mu 2less than or equals nothing. ​(Type an integer or decimal rounded to three decimal places as​ needed.) Interpret the confidence interval. Choose the correct answer below. A. With 10​% ​confidence, the difference between the population mean waiting time between the two banks falls below the lower confidence interval. B. With 90​% ​confidence, the difference between the population mean waiting time between the two banks falls in this interval. C. With 10​% ​confidence, the difference between the population mean waiting time between the two banks falls below the upper confidence level. D. With 90​% ​confidence, the difference between the population mean waiting time between the two banks falls outside this interval.

Answer 1

A. Upper H 0​: mu 1 equals mu 2 Upper H 1​: mu 1 not equals mu 2

T stat = 2.92

B. Reject Upper H 0. There is sufficient evidence that the mean waiting time between the two branches differ

B. It is the probability of obtaining a sample that yields a t test statistic farther away from 0 in the positive direction than the computed test statistic if there is no difference in the mean waiting time between Bank A and Bank B

D. Both sampled populations are approximately normal.

B. With 90​% ​confidence, the difference between the population mean waiting time between the two banks falls in this interval.