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Hypothesis Testing

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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