Hypothesis Testing & Confidence Interval

In the bank customer waiting time case, a bank manager had developed a new system to reduce the time customers spend waiting to be served by tellers during peak business hours. Typical waiting times during peak business hours under the current ystem are roughly 9 to 10 minutes The bank manager hopes that the new system will lower typical waiting times to less than 6 minutes

The mean and standard deviation of the sample of the sample of 100 bank customer waiting times are x-bar = 5.46 minutes and s=2.475 minutes. Let u denote the mean of all possible bank customers waiting times using the new system during peak hours

a) calculate the 90% and 99% confidence intervals of u (to at least 2 decimal places)
b) using the 90% confience interval, can the bank manger be 90% confident that u is less than 6 minutes? Explain your answer.
c) Using the 99% confidence interval,can the bank manager be 99% confident that u is less than 6 minutes? Explain you answer.

Last question:

Cinsider again the same Bank Customer waiting case. Suppose the mnager wishes to use the 100 waiting times to support the claim that the mean waiting time u under the new system is shorter than six minutes. The random sample yields a sample mean x-bar =5.46 minutes and a sample standard deviation of s=2.475 minutes. Fit the answers into each sub section below:

A. The following questions representing the five-step hypothesis testing procedures will help you to decide whether the sample data provides evidence to conclude that the mean waiting time under the new system is shorter than 6 minutes (USING alpha =0.05)

1 Formulate the null and alternative hypotheses

2 Determine the criterion for rejection or non rejection of Ho in terms of critical values.

3 Calculate the test statistic

4 Compare the test statistic to the rejection region and make a judgement about the null and alternative hyootheses

5 Interpret the statistical decision in terms of the problem (original claim)

B

1 Compute the observed p-valuye in the hypothesis test

2 interpret the p-value. What does it mean?

3 Using the p-value, what decision would you make about the null hypothesis Ho? Why?