Question

The manager of a bank is concerned about the amount of time one of her tellers, Kate, 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 Kate 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, Kate 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

H0: Null Hypothesis: 4

HA: Alternative Hypothesis: 4

From the given data, the following statistics are calculated:

n = 10

= 5

s = 1.9437

SE = s/

= 1.9437/

= 0.6147

Test Statistic is given by:

t = (5 - 4)/0.6147

= 1.6269

ndf = n - 1 = 10 - 1 = 9

One Tail - Right Side Test

By Technology, p - value = 0.0691

Since p - value = 0.0691 is greater than = 0.05, the difference is not significant. Fail to reject null hypothesis.

Conclusion:
There is not sufficient evidence to suggest that, on average, Kate exceeds the target service time

We must assume that the population Distribution is Normal Distribution in order for our conclusion to be valid.