# Hypothesis Testing

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Research by the Illinois Banking Company revealed that only 10 percent of their customers wait more than five minutes to do their banking. Management considers this reasonable and will not add more tellers unless the proportion becomes larger than 10 percent. The branch manager at the Litchfield Branch believes that the wait is longer than the standard at her branch and requested additional part-time tellers. To support her request the branch manager reported that in a sample of 100 customers, 14 waited more than five minutes. AT the 0.01 significance level, is it reasonable to conclude that more that 10 percent of the customers wait more than five minutes?

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Solution. We can set up the null hypothesis H0: p=10% and, the alternative hypothesis H1: p is not equal 10%

Define Xi as follows: Xi=1 if the ith customer waited more than 5 minutes, otherwise, Xi=0. i=1,2,...100. We assume ...

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- BSc , Wuhan Univ. China
- MA, Shandong Univ.

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- "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."
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- "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!"
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