4. vP of operations at Portland Trust Bank, is evaluating the service level for

Question

4. vP of operations at Portland Trust Bank, is evaluating the service level for provided to walk-in customers. Brian would like to minimize the variance of waiting time these customers, since this would mean each customer received the same level of service Accordingly, his staff recorded the waiting times for 15 randomly selected walk-in customers and determined that their mean waiting time was 15 minutes and that the standard was minutes. Assume that waiting time is normally distributed. Use this sample information to develop 90% confidence interval for the population variance of waiting times for these customers. What is the point estimate? 5 pts

Explanation / Answer

Sample size, n = 15

Sample mean, X' = 15

Sample SD, S = 4

Here, S2 is used as point estimator, whose value is equal to:

S2 = 4*4 = 16

90% CI for population variance with n-2 ( = 13) degrees of freedom is:

(n-1)*S2/Q0.05 < (s')2 < (n-1)*S2/Q0.95

Here (s')2 denotes the population variance. Q values denote the critical chi-squared values which are determined from chi-distribution table.

Putting values we get:

14*(16/22.362) < (s')2 < 14*(16/5.89)

10.016 < (s')2 < 38.03

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