Question

A local bank claims that the waiting time for its customers to be served is the lowest in the area. A competitor bank checks the waiting times at both banks. The sample statistics are listed below. Test the local bank's claim. Use the information given below. Use the significant level of .05 and assume the variances are equal.

sample size	Local Bank n1 = 46	Competitor Bank n2 = 50
Average waiting time in minutes for each sample	Xbar1 = 2.3 mins	Xbar2 = 2.6 mins
Sample Standard Deviation of each Sample	S1 = 1.1 mins	S2 = 1.0 mins

1. Are the samples dependent or independent?

2. State your Null/Alternative hypotheses

3. What is the test-statistic?

4. What is the p-value?

5. What are the critical values?

6. Does the test-statistic lie in the rejection region?

7. Interpret the result?

8. Does the result change for a different value of alpha? Explain?

Answer 1

	Local Bank	Competitor Bank
Sample Size
Average Waiting Time
Sample Std . Deviation

1 . The two samples are independent as they have different sample sizes . First condition for data to be dependent is the equality of sample sizes which is not the case here .

2 . We define our Null Hypothesis as follows :

:   i.e. , There is no significant difference in Average Waiting Times of the two banks .

VS

i.e. , Waiting time of local bank is significantly less compared to other bank .

3 . Since , we have assumed equality of variances , We could use Two Sample t - test to test the hypothesis .

where ,   is the Pooled Variance and ,

4 . p - Value is the probability of obtaining test result at least as extreme as that observed during the test .

Using the t- distribution tables :

p -Value = 8.527 %

5 . The test is a one - Tailed Test i.e. , Right - Tailed Test .

The tabulated value of   at 5 % level of significance = 1.661 which is the critical value .

6 . The Tabulated value of the Test Statistic ( 1.39975 ) is less than the critical value ( 1.661 ) , so the Test - Statistic doesn't lie in the rejection region .

7 . Since , ( Cal . ) < ( Tab. ) i.e. , 1.39975 < 1.661 , we have insufficient evidence to reject at 5 % level of significance . We could also reach the conclusion using the p - Value .

As , p -Value ( 8.527 % ) is greater than Level of Significance ( 5 % ) , we have insufficient evidence to reject at 5 % level of significance .

So , Local Bank's claim is wrong . There is no significant difference in Average Waiting Times of the two banks .

8 . Yes , the result would change for different values of   .

• As increase , the Test - Statistic would start moving towards the Rejection Region .
• As decrease , the evidence of Null - Hypothesis acceptance becomes more strong as Test - Statistic moves farther from the Rejection Region .