Question

Question: An automatic coffee machine dispenses cups of coffee whose volume per cup varies normally and should have the mean μ = 10 oz if it is working correctly. 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.

In this problem, we have made slight changes to the "coffee machine" story above. In which of the options below is the change such that it would be inappropriate to conduct a hypothesis test for: H₀: μ = 10 vs. H_a: μ < 10. Check all that apply.

~Group of answer choices~

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.

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. 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.

Answer 1

Correct option:

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.

Explanation:

In the above description, we note: (i) The population distribution is not given as Normal Distribution (ii) Population Standard Deviation is not given (iii) Sample Size = n = 8 < 30, Small Sample.

Since Small Sample, t distribution is to be used, which requires population to be Normal Distribution.