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.
Commercial | Residential |
4.35 | 9.88 |
5.54 | 5.77 |
3.01 | 8.06 |
5.24 | 5.79 |
4.76 | 8.64 |
2.34 | 3.58 |
3.64 | 8.12 |
3.24 | 8.63 |
4.44 | 10.46 |
6.16 | 6.55 |
0.14 | 5.56 |
5.17 | 4.15 |
6.46 | 6.13 |
6.37 | 9.88 |
3.55 | 5.27 |
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 α=0.05.).
Let μ1 be the mean waiting time of the commercial district branch and μ2 be the mean waiting time of the residential area branch. Determine the hypotheses.
b. Find the test statistic. (Round to two Decimal places)
c. Find the Critical Values. (Use a comma to separate answers as needed. Round to two decimal places)
d. Determine the p-value in (a) and interpret its meaning.
e. Construct and interpret a 95% confidence interval estimate of the difference between the population means between the two branches. (Round to three decimal places.)
using excel>addin>phstat>two sample test
we have
Pooled-Variance t Test for the Difference Between Two Means | ||||
(assumes equal population variances) | ||||
Data | Confidence Interval Estimate | |||
Hypothesized Difference | 0 | for the Difference Between Two Means | ||
Level of Significance | 0.05 | |||
Population 1 Sample | Data | |||
Sample Size | 15 | Confidence Level | 95% | |
Sample Mean | 4.294 | |||
Sample Standard Deviation | 1.706172827 | Intermediate Calculations | ||
Population 2 Sample | Degrees of Freedom | 28 | ||
Sample Size | 15 | t Value | 2.0484 | |
Sample Mean | 7.098 | Interval Half Width | 1.4534 | |
Sample Standard Deviation | 2.154109693 | |||
Confidence Interval | ||||
Intermediate Calculations | Interval Lower Limit | -4.2574 | ||
Population 1 Sample Degrees of Freedom | 14 | Interval Upper Limit | -1.3506 | |
Population 2 Sample Degrees of Freedom | 14 | |||
Total Degrees of Freedom | 28 | |||
Pooled Variance | 3.7756 | |||
Standard Error | 0.7095 | |||
Difference in Sample Means | -2.8040 | |||
t Test Statistic | -3.9520 | |||
Two-Tail Test | ||||
Lower Critical Value | -2.0484 | |||
Upper Critical Value | 2.0484 | |||
p-Value | 0.0005 | |||
Reject the null hypothesis |
a.Let μ1 be the mean waiting time of the commercial district branch and μ2 be the mean waiting time of the residential area branch. the null and alternative hypothesis are
Ho:μ1 =μ2
Ha:μ1 μ2 (two tailed)
b. the test statistic t = -3.95
c. Find the Critical Values are (-2.05 ,2.05)
d. the p-value is 0.0005 . since p value is less than 0.05 so we reject Ho and conclude that there is a difference in the mean waiting time between the two branches
e. 95% Confidence interval is (-4.257,-1.351)
we are 95% confident that the difference between the population means between the two branches lies between (-4.257,-1.351)
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