Question

1. the owner of a football team claims that the average attendance at games is over 523, 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 nontechnical terms.

a) there is not sufficient evidence to support the claim that the mean attendance is less than 523.
b) there is sufficient evidence to support the claim that the mean attendance is greater than than 523.
c) there is sufficient evidence to support the claim that the mean attendance is less than 523.
d) there is not sufficient evidence to support the claim that the mean attendance is greater than 523.

1. the manufacturer of a refrigerator system for beer kegs produces refrigerators that are supposed to maintain a true mean temperature, μ, of 47°f, ideal for a certain type of german pilsner. the owner of the brewery does not agree with the refrigerator manufacturer, and claims he can prove that the true mean temperature is incorrect. assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms.

a) there is not sufficient evidence to support the claim that the mean temperature is equal to 47°f.
b) there is not sufficient evidence to support the claim that the mean temperature is different from 47°f.
c) there is sufficient evidence to support the claim that the mean temperature is equal to 47°f.
d) there is sufficient evidence to support the claim that the mean temperature is different from 47°f.

1. the principal of a middle school claims that test scores of the seventh - graders at his school vary less than the test scores of the seventh - graders at a neighboring school, which have variation described by σ = 14.7. assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms.

a) there is sufficient evidence to support the claim that the standard deviation is less than 14.7.
b) there is not sufficient evidence to support the claim that the standard deviation is less than 14.7.
c) there is not sufficient evidence to support the claim that the standard deviation is greater than 14.7.
d) there is sufficient evidence to support the claim that the standard deviation is greater than 14.7.
assume that a hypothesis test of the given claim will be conducted. identify the type i or type ii error for the test.

1. the principal of a school claims that the percentage of students at his school that come from single - parent homes is 11%. identify the type ii error for the test.

a) reject the claim that the percentage of students that come from single - parent homes is equal to 11% when that percentage is actually less than 11%.
b) fail to reject the claim that the percentage of students that come from single - parent homes is equal to 11% when that percentage is actually 11%.
c) fail to reject the claim that the percentage of students that come from single - parent homes is equal to 11% when that percentage is actually different from 11%.
d) reject the claim that the percentage of students that come from single - parent homes is equal to 11% when that percentage is actually 11%.

Explanation:

14)

When we fail to reject the null hypothesis, it means we do not have enough evidence to support the alternative hypothesis. The claim here is that the average attendance is over 523 (alternative hypothesis). Failing to reject the null (which would be \(H_0:\mu\leq523\)) means there is not sufficient evidence for the alternative (average attendance > 523).

Rejecting the null hypothesis (\(H_0:\mu = 47^{\circ}F\)) means we have enough evidence to support the alternative hypothesis. The alternative hypothesis here is that the mean temperature is not \(47^{\circ}F\) (since the claim is that the mean is incorrect).

Rejecting the null hypothesis (\(H_0:\sigma\geq14.7\)) means we have enough evidence to support the alternative hypothesis. The alternative hypothesis here is \(\sigma < 14.7\) (claim is that test - scores vary less, i.e., standard deviation is less).

Answer:

D. There is not sufficient evidence to support the claim that the mean attendance is greater than 523.

15)