Suppose the Environmental Protection Agency is in the process of monitoring the water quality in a large estuary in the eastern United States, in order to measure the PCB concentration (in parts per billion).

a. Suppose that a random sample of size 80 has a sample mean of 1.59 ppb and a sample standard deviation of 0.25 ppb. Test the hypothesis, at the 5% level, that the mean PCB concentration in the estuary is less than or equal to 1.50 ppb against the alternative that it is higher. Is H0 rejected?

b. If the population mean is 1.6 ppb and the population standard deviation is 0.33 ppb, what is the probability that the null hypothesis H0: µ ≤ 1.50 is rejected at the 5% level, if the sample size is 80?

c. If the population mean is 1.6 ppb and the population standard deviation is 0.33 ppb, what sample size is needed so that the probability is 0.99 that H0: µ ≤ 1.50 is rejected at the 5% level?