With individual lines at its various windows, a post office finds that the standard deviation for normally distributed waiting times for customers on Friday afternoon is 7.2 minutes. To test this claim, 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 3.5 minutes.
1. With a significance level of 5 percent, conduct an appropriate test on
the claim. (State your null hypothesis, test statistic, critical value, decision rule,
conclusion)
2. What is the 95% confidence interval for the population variance?
You may use the critical values as below:
χ2(0.05,24) = 13.84843 , χ2(0.025,24) = 12.40115 , χ2(0.05,25) = 14.61141 ,
χ2(0.025,25) = 13.11972 , χ2(0.95,24) = 36.41503 , χ2(0.975,24) = 39.36408 ,
χ2(0.95,25) = 37.65248 , χ2(0.975,25) = 40.64647