Question

The owner of a local golf course wants to examine the difference between the average ages of males and females that play on the golf course. Specifically, he wants to test if the average age of males is greater than the average age of females. If the owner conducts a hypothesis test for two independent samples and calculates a p-value of 0.5441, what is the appropriate conclusion? Label males as group 1 and females as group 2.

	1) We did not find enough evidence to say the average age of males is less than the average age of females.
	2) We did not find enough evidence to say a significant difference exists between the average age of males and females.
	3) We did not find enough evidence to say the average age of males is larger than the average age of females.
	4) The average age of males is less than or equal to the average age of females.
	5) The average age of males is significantly larger than the average age of females.

You are looking for a way to incentivize the sales reps that you are in charge of. You design an incentive plan as a way to help increase in their sales. To evaluate this innovative plan, you take a random sample of your reps, and their weekly incomes before and after the plan were recorded. You calculate the difference in income as (after incentive plan - before incentive plan). You perform a paired samples t-test with the following hypotheses: Null Hypothesis: μ_D ≥ 0, Alternative Hypothesis: μ_D< 0. You calculate a p-value of 0.001. What is the appropriate conclusion of your test?

	1) We did not find enough evidence to say there was a significantly negative average difference in weekly income. The incentive plan does not appear to have been effective.
	2) The average difference in weekly income is significantly different from 0. There is a significant difference in weekly income due to the incentive plan.
	3) The average difference in weekly income is significantly less than 0. The average weekly income was higher before the incentive plan.
	4) The average difference in weekly income is significantly larger than 0. The average weekly income was higher after the incentive plan.
	5) The average difference in weekly income is greater than or equal to 0.

It is reported in USA Today that the average flight cost nationwide is $468. You have never paid close to that amount and you want to perform a hypothesis test that the true average is actually different from $468. The hypotheses for this situation are as follows: Null Hypothesis: μ = 468, Alternative Hypothesis: μ ≠ 468. If the true average flight cost nationwide is $468 and the null hypothesis is rejected, did a type I, type II, or no error occur?

	1) We do not know the p-value, so we cannot determine if an error has occurred.
	2) Type II Error has occurred
	3) We do not know the degrees of freedom, so we cannot determine if an error has occurred.
	4) No error has occurred.
	5) Type I Error has occurred.

Answer 1

The Rejection rule using the p value method is Reject H0 if p value < .

If is not mentioned, then we use the default level = 0.05

(a) In this case, the hypothesis is

H0:

Ha: (Claim)

This is a right tailed test.

p value (0.5441) is > , hence we fail to reject H0.

Therefore Option 3: We did not find enough evidence that the average age of males is greater than the average age of females.

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(b) The hypothesis is

H0: 0

Ha: < 0

This is a left tailed test

p value (0.001) is < , hence we reject H0.

Therefore Option 3: The average difference in weekly income is significantly less than 0, The average weekly income was higher before the incentive plan.

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(c) A Type I error is the incorrect rejection of a true null hypothesis, whereas a type II error is the incorrect retention of a false null hypothesis.

In this case the null hypothesis 468 is rejected when actually it is true.

Therefore Option 5: A Type I error has occurred

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