Question

Suppose U.S. consumers 21 years and older consumed 26.2 gallons of beer and cider per person during 2017. A distributor in Milwaukee believes that beer and cider consumption are higher in that city. A sample of consumers 21 years and older in Milwaukee will be taken, and the sample mean 2017 beer and cider consumption will be used to test the following null and alternative hypotheses:

H₀: μ ≤ 26.2

H_a: μ > 26.2

(a)

Assume the sample data led to rejection of the null hypothesis. What would be your conclusion about consumption of beer and cider in Milwaukee?

Conclude that the population mean annual consumption of beer and cider in Milwaukee is greater than 26.2 gallons and hence lower than throughout the United States.

Conclude that the population mean annual consumption of beer and cider in Milwaukee is greater than 26.2 gallons and hence higher than throughout the United States.    

Conclude that the population mean annual consumption of beer and cider in Milwaukee is less than or equal to 26.2 gallons and hence lower than throughout the United States.

Conclude that the population mean annual consumption of beer and cider in Milwaukee is less than or equal to 26.2 gallons and hence higher than throughout the United States.

(b)

What is the Type I error in this situation? What are the consequences of making this error?

The type I error is rejecting H₀ when it is true. This error would claim the consumption in Milwaukee is greater than 26.2 when it is actually less than or equal to 26.2.

The type I error is not rejecting H₀ when it is true. This error would claim the consumption in Milwaukee is less than or equal to 26.2 when it is actually less than or equal to 26.2.    

The type I error is rejecting  H₀  when it is false. This error would claim the consumption in Milwaukee is greater than 26.2 when it is actually greater than 26.2.

The type I error is not rejecting H₀ when it is false. This error would claim the consumption in Milwaukee is less than or equal to 26.2 when it is actually greater than 26.2.

(c)

What is the Type II error in this situation? What are the consequences of making this error?

The type II error is accepting H₀ when it is false. This error would claim that the population mean annual consumption of beer and cider in Milwaukee is less than or equal to 26.2 gallons when it is not.

The type II error is not accepting H₀ when it is true. This error would claim that the population mean annual consumption of beer and cider in Milwaukee is greater than 26.2 gallons when it is not.    

The type II error is not accepting H₀ when it is false. This error would claim that the population mean annual consumption of beer and cider in Milwaukee is greater than 26.2 gallons when it is greater than 26.2.

The type II error is accepting H₀ when it is true. This error would claim that the population mean annual consumption of beer and cider in Milwaukee is less than or equal to 26.2 gallons when it is less than or equal to 26.2.

Answer 1