Question

Two years ago, the average level of a certain noxious chemical at the mouth of the Kentucky River was 180 parts per million. Since then, new water treatment facilities have been added upstream and dumping regulations have been strictly enforced, leading to the belief that the average level of the pollutant has been reduced. To verify this belief, 49 random samples are taken at the mouth of the river. The mean and standard deviation of these samples are, respectively, 162 parts per million (ppm) and 42 ppm. What hypotheses would you test if you want to show that the mean level of this particular pollutant has been reduced? What is the value of the appropriate test statistic for verifying the belief? What is the p-value of the appropriate test for verifying the belief?

Answer 1

H₀: $\mu$ = 180

H₁: $\mu$ < 180

The test statistic t = ($\bar x - \mu$)/(s/$\dpi{100} \sqrt n$)

                             = (162 - 180)/(42/$\dpi{100} \sqrt 49$)

                             = -3

df = 49 - 1 = 48

P-value = P(T < -3)

             = 0.0021