A hypothesis test is to be performed. State the null and alternative hypotheses. -Carter Motor Company claims that its new sedan, the Libra, will average better than 25 miles per gallon, which is the gas mileage of its competitor. A) Null hypothesis: mean gas mileage $ 23 \mathrm { mpg }$ B) Null hypothesis: mean gas mileage $ 23 \mathrm { mpg }$ Alternative hypothesis: mean gas mileage $= 23 \mathrm { mpg }$ C) Null hypothesis: mean gas mileage $= 23 \mathrm { mpg }$ Alternative hypothesis: mean gas mileage $\geq 23 \mathrm { mpg }$ D) Null hypothesis: mean gas mileage $= 23 \mathrm { mpg }$ Alternative hypothesis: mean gas mileage $ 23 \mathrm { mpg }$

Question

A hypothesis test is to be performed. State the null and alternative hypotheses.
-Carter Motor Company claims that its new sedan, the Libra, will average better than 25 miles per gallon, which is the gas mileage of its competitor.
A) Null hypothesis: mean gas mileage $< 23 \mathrm { mpg }$
Alternative hypothesis: mean gas mileage $> 23 \mathrm { mpg }$
B) Null hypothesis: mean gas mileage $> 23 \mathrm { mpg }$
Alternative hypothesis: mean gas mileage $= 23 \mathrm { mpg }$
C) Null hypothesis: mean gas mileage $= 23 \mathrm { mpg }$
Alternative hypothesis: mean gas mileage $\geq 23 \mathrm { mpg }$
D) Null hypothesis: mean gas mileage $= 23 \mathrm { mpg }$
Alternative hypothesis: mean gas mileage $> 23 \mathrm { mpg }$

Quizplus · Accepted Answer

The null hypothesis typically states there is no effect or no difference, so it would be that the gas mileage is equal to the competitor's 25 mpg, not 23 mpg as stated in the options. The alternative hypothesis correctly captures the company's claim of better than 25 mpg. However, since none of the options correctly state the competitor's mileage as 25 mpg, option D is the closest to correct, assuming a typographical error in the options, with the null hypothesis stating equality (no difference) and the alternative hypothesis reflecting an improvement or difference.

A Hypothesis Test Is to Be Performed <23mpg< 23 \mathrm { mpg }<23mpg

A Hypothesis Test Is to Be Performed $< 23 \mathrm { mpg }$