Question

The data table contains waiting times of customers at a bank, where customers enter a single waiting line that feeds three teller windows. Test the claim that the standard deviation of waiting times is less than. 1.5 minutes, which is the standard deviation of waiting times at the same bank when separate waiting lines are used at each teller window. Use the significance level of 0.025.

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Please help with part B and C

C.) find the P value

Answer 1

$H_0:\sigma=1.5~minutes~vs.~H_A:\sigma<1.5~minutes\Leftrightarrow\\ H_0:\sigma^2=1.5^2~minutes^2~vs.~H_A:\sigma^2<1.5^2~minutes^2,~so~the~statistic~is\\ \chi^2=\frac{\sum_{i=1}^n(X_i-\bar{X})^2}{1.5^2}\sim \chi^2_{60-1}=\chi^2_{59}~under~H_0\\ where,~\bar{X}=\frac{1}{60}\sum_{i=1}^{60}X_i=sample~mean~of~waiting~time\\ X_i=waiting~time~of~ith~customer,~i=1(1)60.\\ B.~Therefore,~\chi^2=37.01\\ C.~p-value=P(\chi^2<37.01|\chi^2\sim \chi^2_{59})= 0.0111$