A hypothesis test is to be performed. Describe the two possible outcomes of the test using the context of the givensituation.
-Carter Motor Company claims that its new sedan, the Libra, will average better than 22 miles per gallon, which is the gas mileage of its competitor.
The hypotheses are as follows:
Null hypothesis: mean gas mileage $= 23 \mathrm { mpg }$
Alternative hypothesis: mean gas mileage $ 23 \mathrm { mpg }$
A) Rejecting the null hypothesis means there is evidence that the mean gas mileage is greater than $23 \mathrm { mpg }$.
Failing to reject the null hypothesis means there is insufficient evidence to conclude that the mean gas mileage is greater than $23 \mathrm { mpg }$.
B) Rejecting the null hypothesis means there is evidence that the mean gas mileage is not equal to $23 \mathrm { mpg }$.
Failing to reject the null hypothesis means there is insufficient evidence to conclude that the mean gas mileage is greater than $23 \mathrm { mpg }$.
C) Rejecting the null hypothesis means there is evidence that the mean gas mileage is greater than 23 mpg.
Failing to reject the null hypothesis means there is insufficient evidence to conclude that the mean gas mileage is equal to $23 \mathrm { mpg }$.
D) Rejecting the null hypothesis means there is evidence that the mean gas mileage is greater than $23 \mathrm { mpg }$.
Accepting the null hypothesis means there is evidence to conclude that the mean gas mileage is equal to $23 \mathrm { mpg }$.

Question

A hypothesis test is to be performed. Describe the two possible outcomes of the test using the context of the givensituation.
-Carter Motor Company claims that its new sedan, the Libra, will average better than 22 miles per gallon, which is the gas mileage of its competitor.
The hypotheses are as follows:
Null hypothesis: mean gas mileage $= 23 \mathrm { mpg }$
Alternative hypothesis: mean gas mileage $> 23 \mathrm { mpg }$
A) Rejecting the null hypothesis means there is evidence that the mean gas mileage is greater than $23 \mathrm { mpg }$.
Failing to reject the null hypothesis means there is insufficient evidence to conclude that the mean gas mileage is greater than $23 \mathrm { mpg }$.
B) Rejecting the null hypothesis means there is evidence that the mean gas mileage is not equal to $23 \mathrm { mpg }$.
Failing to reject the null hypothesis means there is insufficient evidence to conclude that the mean gas mileage is greater than $23 \mathrm { mpg }$.
C) Rejecting the null hypothesis means there is evidence that the mean gas mileage is greater than 23 mpg.
Failing to reject the null hypothesis means there is insufficient evidence to conclude that the mean gas mileage is equal to $23 \mathrm { mpg }$.
D) Rejecting the null hypothesis means there is evidence that the mean gas mileage is greater than $23 \mathrm { mpg }$.
Accepting the null hypothesis means there is evidence to conclude that the mean gas mileage is equal to $23 \mathrm { mpg }$.

Quizplus · Accepted Answer

Rejecting the null hypothesis in this context means that there is statistical evidence supporting the claim that the mean gas mileage is greater than 23 mpg, which aligns with the alternative hypothesis. Failing to reject the null hypothesis indicates that there is not enough evidence to support a conclusion that the mean gas mileage exceeds 23 mpg, but it does not prove the mean gas mileage is exactly 23 mpg.

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

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