Suppose the EPA is in the process of monitoring the water quality in a large est

Question

Suppose the EPA is in the process of monitoring the water quality in a large estuary in the eastern United States, in order to measure the polychlorinated biphenyl (PCB) concentration in parts per billion (ppb). 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. Is there evidence that the mean PCB concentration in the estuary is higher than 1.50 ppb? Test at the 10% level.

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Suppose the EPA is in the process of monitoring the water quality in a large estuary in the eastern United States, in order to measure the polychlorinated biphenyl (PCB) concentration in parts per billion (ppb). 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. Is there evidence that the mean PCB concentration in the estuary is higher than 1.50 ppb? Test at the 10% level. a) State the hypotheses. b) Check the necessary assumptions. c) Calculate the test statistic. d) Find the p-value. e) Make a decision f) State the conclusion. g) Construct an appropriate confidence interval (CI) to test the hypotheses. State the decision based on 2. the Cl. Does your decision match the decision in (e)?

Explanation / Answer

given that

mean = 1.59 n = 80 and sd = 0.25

The hypothesis

H0 : The mean PCB concentration in the estuary is not higher than 1.50ppb
H1 : The mean PCB concentration in the estuary is higher than 1.50ppb

The test statistic is

T = (xbar-mu)/(sd/sqrt(n))
t = (1.59-1.50)/(0.25/sqrt(80)) = 3.219

now we check the p value from the t table for 1 tail test as the test is directional
df = 80-1 = 79 and alpha = 0.1
The P-Value is .000934.

The result is significant at p < .10

as the p value is less than 0.1 , hence we reject the null hypothesis and conclude that The mean PCB concentration in the estuary is higher than 1.50ppb

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