Question

Question 10 (1 point)

A new gasoline additive is supposed to make gas burn more cleanly and increase gas mileage in the process. Consumer Protection Anonymous conducted a mileage test to confirm this. They took a sample of their cars, filled it with regular gas, and drove it on I-94 until it was empty. They repeated the process using the same cars, but using the gas additive. Using the data they found, they performed a paired t-test with data calculated as (with additive - without additive) with the following hypotheses: Null Hypothesis: μ_D ≤ 0, Alternative Hypothesis: μ_D > 0. If they calculate a p-value of 0.0236 in the paired samples t-test, what is the appropriate conclusion?

Question 10 options:

	1) The average difference in gas mileage is significantly less than 0. The average gas mileage was higher without the additive.
	2) We did not find enough evidence to say there was a significantly positive average difference in gas mileage. The additive does not appear to be effective.
	3) The average difference in gas mileage is significantly different from 0. There is a significant difference in gas mileage with and without the additive.
	4) The average difference in gas mileage is less than or equal to 0.
	5) The average difference in gas mileage is significantly larger than 0. The average gas mileage was higher with the additive.

Question 11 (1 point)

A new gasoline additive is supposed to make gas burn more cleanly and increase gas mileage in the process. Consumer Protection Anonymous conducted a mileage test to confirm this. They took a sample of their cars, filled it with regular gas, and drove it on I-94 until it was empty. They repeated the process using the same cars, but using the gas additive. Using the data they found, they performed a paired t-test with data calculated as (with additive - without additive) with the following hypotheses: Null Hypothesis: μ_D = 0, Alternative Hypothesis: μ_D ≠ 0. If they calculate a p-value of 0.4164 in the paired samples t-test, what is the appropriate conclusion?

Question 11 options:

	1) We did not find enough evidence to say the average difference in gas mileage was not 0. The additive does not appear to have been effective.
	2) We did not find enough evidence to say there was a significantly negative average difference in gas mileage. The additive does not appear be effective.
	3) The average difference in gas mileage is equal to 0.
	4) The average difference in gas mileage is significantly different from 0. There is a significant difference in gas mileage with and without the additive.
	5) We did not find enough evidence to say there was a significantly positive average difference in gas mileage. The additive does not appear to be effective.

Question 12 (1 point)

In the year 2000, the average car had a fuel economy of 24 MPG. You are curious as to whether the average in the present day is greater than the historical value. The hypotheses for this scenario are as follows: Null Hypothesis: μ ≤ 24, Alternative Hypothesis: μ > 24. If the true average fuel economy today is 26.4 MPG and the null hypothesis is rejected, did a type I, type II, or no error occur?

Question 12 options:

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

Question 13 (1 point)

In the year 2000, the average car had a fuel economy of 23.8 MPG. You are curious as to whether the average in the present day is less than the historical value. The hypotheses for this scenario are as follows: Null Hypothesis: μ ≥ 23.8, Alternative Hypothesis: μ < 23.8. If the true average fuel economy today is 33.2 MPG 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 degrees of freedom, so we cannot determine if an error has occurred.
	2) No error has occurred.
	3) We do not know the p-value, so we cannot determine if an error has occurred.
	4) Type I Error has occurred.
	5) Type II Error has occurred

Answer 1

10) option - 5

11) option- 1

12) option- 1

13) option- 3

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