Question

A bank with branches located in a commercial district of a city and in a residential area has the business objective of developing an improved process for serving customers during the noon-to-1 P.M. lunch period. Management decides to first study the waiting time in the current process. The waiting time is defined as the number of minutes that elapses from when the customer enters the line until he or she reaches the teller window. Data are collected from a random sample of 15 customers at each branch. Complete parts (a) through (d) below. Commercial Residential 4.28 9.73 5.61 5.85 3.18 8.06 5.41 5.67 4.68 8.65 2.42 3.74 3.39 8.16 3.18 8.57 4.27 10.69 6.14 6.71 0.03 5.74 5.12 4.05 6.58 6.25 6.29 9.97 3.93 5.33 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 0.01.) Let mu 1 be the mean waiting time of the commercial district branch and mu 2 be the mean waiting time of the residential area branch. Determine the hypotheses. Choose the correct answer below. A. Upper H0: mu 1 greater than or equals mu 2 Upper H1: mu 1 less than mu 2 B. Upper H0: mu 1 not equals mu 2 Upper H1: mu 1 equals mu 2 C. Upper H0: mu 1 less than or equals mu 2 Upper H1: mu 1 greater than mu 2 D. Upper H0: mu 1 equals mu 2 Upper H1: mu 1 not equals mu 2 Find the test statistic. t Subscript STAT equals nothing (Round to two decimal places as needed.) Find the critical value(s). nothing (Use a comma to separate answers as needed. Round to two decimal places as needed.) Choose the correct conclusion below. A. Do not reject Upper H0. There is insufficient evidence that the mean waiting time between the two branches differ. B. Reject Upper H0. There is insufficient evidence that the mean waiting time between the two branches differ. C. Reject Upper H0. There is sufficient evidence that the mean waiting time between the two branches differ. D. Do not reject Upper H0. 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-value equals nothing (Round to three 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 the negative direction than the computed test statistic if there is no difference in the mean waiting time between commercial and residential banks. 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 commercial and residential banks. C. It is the probability the two banks have different population mean waiting times. D. 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 commercial and residential banks. c. In addition to equal variances, what other assumption is necessary in (a)? A. The sample sizes must be equal. B. Both sampled populations are not approximately normal. C. The samples are specifically chosen and not independently sampled. D. Both sampled populations are approximately normal. d. Construct and interpret a 99% confidence interval estimate of the difference between the population means between the two branches. The 99% confidence interval is nothing less than or equals mu 1 minus mu 2 less than or equals nothing. (Round to three decimal places as needed.) Interpret the confidence interval. Choose the correct answer below. A. With 99% confidence, the difference between the population mean waiting time between the two banks falls in this interval. B. With 1% confidence, the difference between the population mean waiting time between the two banks falls below the lower confidence interval limit. C. With 1% confidence, the difference between the population mean waiting time between the two banks falls above the upper confidence interval limit. D. With 99% confidence, the difference between the population mean waiting time between the two banks falls outside this interval.

Name: a bank with branches located in a commercial district of a city and in a residential area has the business objective of developing an improved process for serving customers during the noon t 43158
Uploaded: 2023-09-21T14:52:50-08:00
Duration: 6 min 3 s
Channel: Sheryl Ezze
Description: a bank with branches located in a commercial district of a city and in a residential area has the business objective of developing an improved process for serving customers during the noon t 43158

Commercial Residential
4.28 9.73
5.61 5.85
3.18 8.06
5.41 5.67
4.68 8.65
2.42 3.74
3.39 8.16
3.18 8.57
4.27 10.69
6.14 6.71
0.03 5.74
5.12 4.05
6.58 6.25
6.29 9.97
3.93 5.33

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 0.01.) Let mu 1 be the mean waiting time of the commercial district branch and mu 2 be the mean waiting time of the residential area branch. Determine the hypotheses. Choose the correct answer below.

A. Upper H0: mu 1 greater than or equals mu 2
Upper H1: mu 1 less than mu 2

B. Upper H0: mu 1 not equals mu 2
Upper H1: mu 1 equals mu 2

C. Upper H0: mu 1 less than or equals mu 2
Upper H1: mu 1 greater than mu 2

D. Upper H0: mu 1 equals mu 2
Upper H1: mu 1 not equals mu 2

Find the test statistic. t Subscript STAT equals nothing (Round to two decimal places as needed.)

Find the critical value(s). nothing (Use a comma to separate answers as needed. Round to two decimal places as needed.)

Choose the correct conclusion below.

A. Do not reject Upper H0. There is insufficient evidence that the mean waiting time between the two branches differ.

B. Reject Upper H0. There is insufficient evidence that the mean waiting time between the two branches differ.

C. Reject Upper H0. There is sufficient evidence that the mean waiting time between the two branches differ.

D. Do not reject Upper H0. 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-value equals nothing (Round to three 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 the negative direction than the computed test statistic if there is no difference in the mean waiting time between commercial and residential banks.

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 commercial and residential banks.

C. It is the probability the two banks have different population mean waiting times.

D. 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 commercial and residential banks.

c. In addition to equal variances, what other assumption is necessary in (a)?

A. The sample sizes must be equal.

B. Both sampled populations are not approximately normal.

C. The samples are specifically chosen and not independently sampled.

D. Both sampled populations are approximately normal.

d. Construct and interpret a 99% confidence interval estimate of the difference between the population means between the two branches. The 99% confidence interval is nothing less than or equals mu 1 minus mu 2 less than or equals nothing. (Round to three decimal places as needed.)

Interpret the confidence interval. Choose the correct answer below.

A. With 99% confidence, the difference between the population mean waiting time between the two banks falls in this interval.

B. With 1% confidence, the difference between the population mean waiting time between the two banks falls below the lower confidence interval limit.

C. With 1% confidence, the difference between the population mean waiting time between the two banks falls above the upper confidence interval limit.

D. With 99% confidence, the difference between the population mean waiting time between the two banks falls outside this interval.

Added by Karen M.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Sheryl Ezze

09/21/2023

Step 1

The hypotheses are: Upper H0: mu1 = mu2 (there is no difference in the mean waiting time between the two branches) Upper H1: mu1 ≠ mu2 (there is a difference in the mean waiting time between the two branches) The test statistic is: tSTAT = -3.05 The critical Show more…

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A bank with branches located in a commercial district of a city and in a residential area has the business objective of developing an improved process for serving customers during the noon-to-1 P.M. lunch period. Management decides to first study the waiting time in the current process. The waiting time is defined as the number of minutes that elapses from when the customer enters the line until he or she reaches the teller window. Data are collected from a random sample of 15 customers at each branch. Complete parts (a) through (d) below. Commercial Residential 4.28 9.73 5.61 5.85 3.18 8.06 5.41 5.67 4.68 8.65 2.42 3.74 3.39 8.16 3.18 8.57 4.27 10.69 6.14 6.71 0.03 5.74 5.12 4.05 6.58 6.25 6.29 9.97 3.93 5.33 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 0.01.) Let mu 1 be the mean waiting time of the commercial district branch and mu 2 be the mean waiting time of the residential area branch. Determine the hypotheses. Choose the correct answer below. A. Upper H0: mu 1 greater than or equals mu 2 Upper H1: mu 1 less than mu 2 B. Upper H0: mu 1 not equals mu 2 Upper H1: mu 1 equals mu 2 C. Upper H0: mu 1 less than or equals mu 2 Upper H1: mu 1 greater than mu 2 D. Upper H0: mu 1 equals mu 2 Upper H1: mu 1 not equals mu 2 Find the test statistic. t Subscript STAT equals nothing (Round to two decimal places as needed.) Find the critical value(s). nothing (Use a comma to separate answers as needed. Round to two decimal places as needed.) Choose the correct conclusion below. A. Do not reject Upper H0. There is insufficient evidence that the mean waiting time between the two branches differ. B. Reject Upper H0. There is insufficient evidence that the mean waiting time between the two branches differ. C. Reject Upper H0. There is sufficient evidence that the mean waiting time between the two branches differ. D. Do not reject Upper H0. 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-value equals nothing (Round to three 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 the negative direction than the computed test statistic if there is no difference in the mean waiting time between commercial and residential banks. 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 commercial and residential banks. C. It is the probability the two banks have different population mean waiting times. D. 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 commercial and residential banks. c. In addition to equal variances, what other assumption is necessary in (a)? A. The sample sizes must be equal. B. Both sampled populations are not approximately normal. C. The samples are specifically chosen and not independently sampled. D. Both sampled populations are approximately normal. d. Construct and interpret a 99% confidence interval estimate of the difference between the population means between the two branches. The 99% confidence interval is nothing less than or equals mu 1 minus mu 2 less than or equals nothing. (Round to three decimal places as needed.) Interpret the confidence interval. Choose the correct answer below. A. With 99% confidence, the difference between the population mean waiting time between the two banks falls in this interval. B. With 1% confidence, the difference between the population mean waiting time between the two banks falls below the lower confidence interval limit. C. With 1% confidence, the difference between the population mean waiting time between the two banks falls above the upper confidence interval limit. D. With 99% confidence, the difference between the population mean waiting time between the two banks falls outside this interval.