Statistics Problem: Mean Wait Time
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A bank manager has developed a new system to reduce the time customers spend waiting for teller service during peak hours. The manager hopes that the new system will reduce waiting times from the current 9 to 10 minutes to less than 6 minutes. Suppose that the manager wishes to use 100 waiting times to support the claim that the mean waiting time under the new system is shorter than six minutes. The random sample of 100 waiting times yields a sample mean of 5.46 minutes. Further, let's assume that the population standard deviation is 2.475.
a) State the null and alternative hypotheses, letting u represent the mean waiting time under the new system.
b) Select the distribution to use. Explain briefly why you selected it.
c) Assuming that she wishes to test the claim at alpha = 0.05, determine the rejection and non-rejection regions based on your hypotheses in (a). State the critical value.
d) Calculate the value of the test statistic.
e) What do you conclude about whether the new system has reduced the mean waiting time to below six minutes? Explain your conclusion in words.
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Solution Summary
The mean wait time is examined for statistics problems.
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a) H0: u >= 6 and Ha: u < 6
b) As the population standard deviation is ...
Education
- BSc , Wuhan Univ. China
- MA, Shandong Univ.
Recent Feedback
- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
- "Thank you very much for your valuable time and assistance!"
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