Question 9.385

34. Price of Milk. The U.S. Bureau of Labor Statistics reports that the mean price for a gallon of milk in June 2014 was $3.63. Suppose that we have a random sample taken this year of 400 gallons of milk, and assume that the population standard deviation equals $1.00. We want to conduct a hypothesis test, using level of significance , to investigate if the population mean price of milk this year has increased.

  1. Describe what a Type II error would mean in the context of this problem.
  2. What is the probability of making a Type II error when the actual mean price takes the following values?
    1. $3.70
    2. $3.90
    3. $4.10
    4. $4.30
  3. Calculate the power of the hypothesis test for the values of given in (b).
  4. Construct the power curve for the values of given in (b).