The water management agency in charge of the lake (in Exercise 11) decides that it would suffice if the probability of exceeding the 100 mg/L threshold was less than 20%. In a random sample of eight...

The water management agency in charge of the lake (in Exercise 11) decides that it would suffice if the probability of exceeding the 100 mg/L threshold was less than 20%. In a random sample of eight water specimens, only one exceeded the threshold. What should the agency conclude if they use a significance level of 5%?

Exercise 11

Lakes where chlorophyll levels exceed 100 mg/L are at risk for fish kills on cloudy days. In a random sample of eight water specimens, the mean chlorophyll level was 91.6 mg/L. Assume that the data come from a normal distribution with σ =20. We want to demonstrate that the mean in this lake is less than the 100 mg/L threshold.

(a) Carry out the test using α = 5%. Include a sketch of the rejection region in your answer.

(b) Calculate the p value. Include a sketch of the relevant area in your answer.