A certain chemical pollutant in the Genesee River has been constant for several years with a mean of 34 ppm (parts per million) and variance of 64 ppm. A group of environmentalists is concerned that the new factory,
which discharges liquids into the river, has increased the amount of pollutant in the river. The
environmentalists’ sample of 50 vials gives a mean of 35.5 ppm. Test if the amount of pollutant in the river has
increased at the 5% level of significance. 

a. Give the null hypothesis using the correct symbol(s). 

b. Give the alternative (also using the correct symbol). Decide if you need a 1-tail or a 2-tail test. 

c. What is(are) the critical value(s)? Use the correct symbol. 

d. Write the equation for the appropriate statistical test using correct symbols. 

e. Calculate the appropriate statistical test (to the hundredth place). 

f. What is your statistical conclusion? 

g. Write an English sentence explaining what you now believe about the new factory and the
pollutants in the river. 

h. Given your answer in part f, which kind of error might you have made? Explain in a sentence or two. 1

i. Using the sample mean as a specific alternative hypothesis (H1 mean) and the critical value you
used in c., calculate the power. (Assume ? is the same in both distributions.) Sketch the
distributions and mark all values there. 

j. How many vials would you need in the sample to have a power of 80%? (Assume ? is the same in
both distributions.) 

k. Using N calculated in j. test again if the amount of pollutant in the river has increased (at the 5%
level of significance). 2