An automatic coffee machine dispenses cups of coffee whose volume per cup varies normally with the mean mu = 10 oz. A quality-control researcher randomly selects 8 cups of coffee from the machine and finds that in this sample the mean volume is 9.92 oz. and the standard deviation is 0.23 oz.

1. Do these data provide enough evidence to conclude that the mean volume per cup is below the target level?

   Which of the following two outputs represents the correct way to conduct this test?
   
   Output A:
   
   Output B:
   
   

   • Output A
   • Output B

2. Which of the following represents the correct conclusion we can make based on the output you selected in the previous problem (and at the usual significance level of .05)?
   
   

   • The data provide enough evidence to reject H₀ and to conclude that the mean volume per cup is lower than the target level of 10 oz.
   • The data provide enough evidence to accept H₀ and to conclude that the mean volume per cup is at the target level of 10 oz.
   • The data do not provide enough evidence to reject H₀, so we accept it, and conclude that the mean volume per cup is at the target level of 10 oz.
   • The data do not provide enough evidence to reject H₀, nor to conclude that the mean volume per cup is lower than the target level of 10 oz.

3. While it is important for you to know how to apply the methods that are covered in this course, it is also important to be able to recognize situations when none of the methods is appropriate. In this problem, we have made slight changes to the "coffee machine" story.
   
   Your task is to recognize in which of the options below the changes are such that none of the methods covered in this course can be applied for testing H₀ mu = 10 vs. H_a mu < 10.
   
   

   • An automatic coffee machine dispenses cups of coffee whose volume per cup varies according to a distribution with mean μ = 10 oz. A quality-control researcher randomly selects 8 cups of coffee from the machine and finds that in this sample the mean volume is 9.92 oz. and the standard deviation is 0.23 oz.
   • An automatic coffee machine dispenses cups of coffee whose volume per cup varies according to a distribution with mean μ = 10 oz. A quality-control researcher randomly selects 40 cups of coffee from the machine and finds that in this sample the mean volume is 9.92 oz. and the standard deviation is 0.23 oz.
   • An automatic coffee machine dispenses cups of coffee whose volume per cup varies normally with mean μ = 10 oz. and standard deviation σ = 0.23 oz. A quality-control researcher randomly selects 8 cups of coffee from the machine and finds that in this sample the mean volume is 9.92 oz.
   • An automatic coffee machine dispenses cups of coffee whose volume per cup varies according to a distribution with mean μ = 10 oz. and standard deviation σ = 0.23 oz. A quality-control researcher randomly selects 8 cups of coffee from the machine and finds that in this sample the mean volume is 9.92 oz.
   • Both (A) and (D) are cases where we cannot run the test using the methods covered in this course.