Question

The manager of a bank is concerned about the amount of time one of her tellers, Keon, needs in order to provide service to a single customer. The reason for her concern is that slow service times result in unacceptable waiting times for customers. The target time to provide service to a single customer is 4 minutes. The owner selects a random sample of 10 customer transactions with Keon and records the time it takes for him to complete each transaction. The times, in minutes, are as follows:

6 9 3 4 5 6 4 2 6 5

Is there sufficient evidence to suggest that, on average, Keon exceeds the target service time? Use the p-value method to conduct an appropriate hypothesis test at the 5% level of significance. What must you assume is true in order for your conclusion to be valid?

Answer 1

First we need to find the mean and standard deviation of data. Following table shows the calculations:

	X	(X-mean)^2
	6	1
	9	16
	3	4
	4	1
	5	0
	6	1
	4	1
	2	9
	6	1
	5	0
Total	50	34

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Conclusion: There is  sufficient evidence to suggest that, on average, Keon exceeds the target service time.

Assumption: Since sample size is small so we must assume that data is normally distributed.