Question

A bank wishes to investigate how long it takes customers to do their business (waiting time and time to perform their transactions, which we call serving time). They believe that average serving time is consistent with 2 minutes per customer being “processed" through the system (during the midmorning hours). A consulting firm is hired by the bank, which observes midmorning operations for a while. They report back that during the survey, 40 customers were served, with the average serving time being 3 minutes, and sample standard deviation of serving time being 1.5 minutes.

a. ( 3 points) The bank wishes to know if these results are consistent with their prior beliefs about the serving process. Carefully state the null and alternative hypotheses that would be appropriate for such a test.

b. (7 points) Carry out an appropriate test at 5% level of significance. What are your conclusions? Justify your answer.

c.  ( 3 points) What is the p-value of the test? Show your work.

Answer 1

(a) The hypothesis being tested is:

H₀: µ = 2

H_a: µ ≠ 2

(b) The test statistic, t = (x - µ)/s/√n

t = (3 - 2)/1.5/√40

t = 4.216

(c) The p-value is 0.0001.

Since the p-value (0.0001) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that the average serving time is not consistent with 2 minutes per customer being “processed" through the system.

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