Question

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 0.0236. What is the appropriate conclusion of your test?

Question 12 options:

1)	The average difference in weekly income is significantly different from 0. There is a significant difference in weekly income due to the incentive plan.

2)	The average difference in weekly income is significantly larger than 0. The average weekly income was higher after the incentive plan.

3)	We did not find enough evidence to say there was a significantly positive average difference in weekly income. The incentive plan does not appear to have been effective.

4)	The average difference in weekly income is significantly less than 0. The average weekly income was higher before the incentive plan.

5)	The average difference in weekly income is less than or equal to 0.

Consumers Energy states that the average electric bill across the state is $48.9. You want to test the claim that the average bill amount is actually greater than $48.9. The hypotheses for this situation are as follows: Null Hypothesis: μ ≤ 48.9, Alternative Hypothesis: μ > 48.9. If the true statewide average bill is $45.74 and the null hypothesis is rejected, did a type I, type II, or no error occur?

Question 13 options:

1)	We do not know the p-value, so we cannot determine if an error has occurred.

2)	Type I Error has occurred.

3)	We do not know the degrees of freedom, so we cannot determine if an error has occurred.

4)	Type II Error has occurred

5)	No error has occurred.

A medical researcher wants to determine if the average hospital stay of patients that undergo a certain procedure is greater than 9.8 days. The hypotheses for this scenario are as follows: Null Hypothesis: μ ≤ 9.8, Alternative Hypothesis: μ > 9.8. If the actual mean is 26.9 days and the null hypothesis is not rejected, did a type I, type II, or no error occur?

Question 14 options:

1)	Type I Error has occurred

2)	No error has occurred.

3)	We do not know the degrees of freedom, so we cannot determine if an error has occurred.

4)	We do not know the p-value, so we cannot determine if an error has occurred.

5)	Type II Error has occurred.

Answer 1

Q13. Given hypothesis testing problem is

The actual mean is 26.9 days and the null hypothesis is not rejected.

The type of error occurs is type II error.

Type II error occurs when we unable to reject the null hypothesis when it is false.

Here we unable to reject the null hypothesis which is false. Hence type II error occurs.