Statistics Question

Question

With individual lines at its various windows, a post office finds that the standard deviation for waiting times for customers on Friday afternoon is 8.2 minutes. The post office experiments with a single, main waiting line and finds that for a random sample of 25 customers, the waiting times for customers have a standard deviation of 4.5 minutes on a Friday afternoon. At the 0.05 level of significance, does this result indicate that a single line causes lower variation among waiting times for customers?

I was able to state the null and alternative hypotheses. I was also able to find the test statistic, which is 7.23. The only question I am confused on is this one: Using alpha = 0.05, what is your conclusion regarding the null and alternative hypotheses?

Answer 1

What is the p-value of the test statistic? If the p-value is less than alpha, then the null hypothesis is rejected. Alternatively, what is the critical value for the test statistic? If the test statistic lies in the critical region (less than the critical value for a left-sided test), then the null hypothesis is rejected.