The owner of a football team claims that the average attendance at home games is over 3000, and he is therefore justified in moving the team to a city with a larger stadium. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is failure to reject the null hypothesis, state the conclusion in non-technical terms.
A. There is sufficient evidence to support the claim that the mean attendance is greater than 3000.
B. There is sufficient evidence to support the claim that the mean attendance is equal to 3000.
C. There is not sufficient evidence to support the claim that the mean attendance is greater than 3000.
D. There is not sufficient evidence to support the claim that the mean attendance is less than 3000.
The null hypothesis is generally an equality, which makes it:
H0: The average attendance at home games equals 3000.
However, when the alternative hypothesis is one sided, which in this case is:
H1: The average attendance at home games is less than 3000.
It will be understood that H0 takes the ≥ sign, or H0: attendance ≥3000.
A failure to reject the null hypothesis is a weak conclusion, while rejecting the null hypothesis is a strong one.
For a weak conclusion, we state that we "fail to reject" the null hypothesis, instead of "accept" the null hypothesis.
From here, there should be sufficient information for you to make the choice.
To determine the conclusion in non-technical terms, we need to understand the concept of the null hypothesis in hypothesis testing. The null hypothesis states that there is no significant difference between the claimed value and the population parameter being tested.
In this case, the owner claims that the average attendance at home games is over 3000. The null hypothesis would be that the mean attendance is not significantly different from 3000.
If the conclusion of the hypothesis test is a failure to reject the null hypothesis, it means that there is not sufficient evidence to support the claim that the mean attendance is greater than 3000. Therefore, the correct conclusion in non-technical terms would be:
C. There is not sufficient evidence to support the claim that the mean attendance is greater than 3000.