An executive at Bank A is concerned that the bank is losing customers because mo

Question

An executive at Bank A is concerned that the bank is losing customers because mortgage applications are taking too long to be approved. The national average, according to an industry newsletter, is six business days. If the executive decides that this bank is taking longer than the national average then she will make major changes to the mortgage department, including demoting or firing the department head. She instructs a vicepresident to investigate the situation. The VP collects a random sample of 12 recent mortgage applications from 9 of the bank’s many branches. The time to process each application (number of business days) is recorded. The 108 observations are listed below.

Bank A

8, 6, 7, 7, 3, 12, 11, 11, 7, 7, 8, 3, 5, 5, 6, 9, 6, 4, 3, 4, 4, 9, 7, 8, 8, 7, 6, 9, 8, 7, 7, 6, 4, 5, 5, 2, 7, 9, 11, 8, 5, 7, 9, 8, 9, 4, 7, 2, 11, 9, 6, 8, 2, 5, 5, 9, 8, 7, 4, 2, 6, 9, 8, 9, 7, 6, 10, 5, 10, 7, 9, 6, 8, 10, 5, 9, 5, 5, 9, 5, 4, 11, 10, 5, 7, 9, 11, 5, 5, 10, 7, 5, 11, 10, 12, 8, 8, 4, 6, 8, 6, 7, 7, 12, 5, 6, 8, 7.

To further investigate the bank’s record on processing mortgage applications, the executive asked the VP to make a comparison with their major competitor, the Bank B. The VP collected a random sample of 108 mortgage processing times for that bank. Perform a twosample t test in Excel to determine if there is a significant difference in processing times at the two banks.

Bank B

6, 6, 7, 6, 6, 4, 5, 8, 3, 7, 9, 6, 6, 4, 8, 5, 7, 6, 6, 7, 3, 10, 6, 7, 5, 9, 9, 6, 7, 2, 6, 8, 4, 4, 6, 8, 6, 2, 11, 6, 5, 6, 9, 6, 7, 6, 4, 7, 5, 5, 5, 3, 6, 11, 4, 7, 7, 6, 5, 7, 10, 6, 4, 4, 2, 6, 6, 7, 3, 4, 9, 7, 9, 10, 6, 4, 5, 5, 4, 5, 6, 6, 7, 3, 8, 12, 2, 7, 8, 7, 9, 8, 9, 3, 9, 7, 5, 3, 7, 3, 3, 7, 4, 9, 3, 8, 9, 9.

1) Should the VP conduct a onesided test or a twosided test? Explain.

2) State the null and alternative hypotheses.

3) Conduct the twosample test in Excel and make sure to include your Excel output.

4) State the Pvalue of the test. Are the data statistically significant at the = 0.05 level? Explain why or why not.

5) State the conclusion of the significance test in context.

Explanation / Answer

1) Since the bank is considering bank B's data also, the test should be a one sided test.

2) H0: the average of both the banks is same.

H1: Bank A'a averge> Bank B

3)

4) p value is 0.005. Since this is less than 0.5, we reject the null hypothesis and conclude that bank A's average is > bank B

5) Bank A's avergae is > bank B.

t-Test: Two-Sample Assuming Equal Variances bank A bank B Mean 6.968519 6.157407 Variance 6.092084 4.713309 Observations 108 108 Pooled Variance 5.402696 Hypothesized Mean Difference 0 df 214 t Stat 2.564318 P(T<=t) one-tail 0.005511 t Critical one-tail 1.652005

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