Respuesta :
Answer:
Option D is correct.
Rejecting the null hypothesis means that;
There is sufficient evidence to support the claim that the mean is greater than 32 miles per gallon.
Step-by-step explanation:
For hypothesis testing, the first thing to define is the null and alternative hypothesis.
In hypothesis testing, especially one comparing two sets of data, the null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test. It usually maintains that, with random chance responsible for the outcome or results of any experimental study/hypothesis testing, its statement is true.
The alternative hypothesis usually confirms the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test. It usually maintains that significant factors other than random chance, affect the outcome or results of the experimental study/hypothesis testing and result in its own statement.
For this question, Carter Motor Company claims that its new sedan, the Libra, will average better than 32 miles per gallon in the city. And since this is talking distance covered per gallon of fuel, better means that the new sedan will average more than 32 miles per gallon.
So, the null hypothesis negating this claim would be that there isn't significant evidence to conclude that the average of the new sedan will be better or greater than 32 miles per gallon.
That is, the new average will be less than or equal to 32 miles per hour.
And the alternative hypothesis will confirm the claim that there is significant evidence to conclude that the average of the new sedan will be better or greater than 32 miles per gallon.
Mathematically,
The null hypothesis is represented as
H₀: μ ≤ 32 miles per gallon
The alternative hypothesis is given as
Hₐ: μ > 32 miles per gallon
So, after the hypothesis test has been conducted, rejecting the null hypothesis means accepting the alternative hypothesis and its statement that there is significant evidence to conclude that the average of the new sedan will be better or greater than 32 miles per gallon.
Hence, option D is correct.
Hope this Helps!!!
