Suppose U.S. consumers 21 years and older consumed 26.2 gallonsof beer and cider per person during 2017. A distributor inMilwaukee believes that beer and cider consumption are higher inthat city. A sample of consumers 21 years and older in Milwaukeewill be taken, and the sample mean 2017 beer and cider consumptionwill be used to test the following null and alternativehypotheses:
H0: μ ≤ 26.2
Ha: 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 ciderin Milwaukee?
Conclude that the population mean annual consumption of beer andcider in Milwaukee is greater than 26.2 gallons and hence lowerthan throughout the United States.
Conclude that the population mean annual consumption of beer andcider in Milwaukee is greater than 26.2 gallons and hence higherthan throughout the United States.   Â
Conclude that the population mean annual consumption of beer andcider in Milwaukee is less than or equal to 26.2 gallons and hencelower than throughout the United States.
Conclude that the population mean annual consumption of beer andcider in Milwaukee is less than or equal to 26.2 gallons and hencehigher than throughout the United States.
(b)
What is the Type I error in this situation? What are theconsequences of making this error?
The type I error is rejecting H0when it is true. This error would claim the consumption inMilwaukee is greater than 26.2 when it is actually less than orequal to 26.2.
The type I error is not rejectingH0 when it is true. This error wouldclaim the consumption in Milwaukee is less than or equal to 26.2when it is actually less than or equal to26.2.   Â
The type I error isrejecting  H0  whenit is false. This error would claim the consumption in Milwaukee isgreater than 26.2 when it is actually greater than 26.2.
The type I error is not rejectingH0 when it is false. This error wouldclaim the consumption in Milwaukee is less than or equal to 26.2when it is actually greater than 26.2.
(c)
What is the Type II error in this situation? What are theconsequences of making this error?
The type II error is accepting H0when it is false. This error would claim that the population meanannual consumption of beer and cider in Milwaukee is less than orequal to 26.2 gallons when it is not.
The type II error is not acceptingH0 when it is true. This error wouldclaim that the population mean annual consumption of beer and ciderin Milwaukee is greater than 26.2 gallons when it isnot.   Â
The type II error is not acceptingH0 when it is false. This error wouldclaim that the population mean annual consumption of beer and ciderin Milwaukee is greater than 26.2 gallons when it is greater than26.2.
The type II error is accepting H0when it is true. This error would claim that the population meanannual consumption of beer and cider in Milwaukee is less than orequal to 26.2 gallons when it is less than or equal to 26.2.
