Question

In the year 2000, the average car had a fuel economy of 24.6 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 ≤ 24.6, Alternative Hypothesis: μ > 24.6. If the true average fuel economy today is 39.2 MPG and the null hypothesis is rejected, did a type I, type II, or no error occur?

Question 16 options:

	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.

As of 2012, the proportion of students who use a MacBook as their primary computer is 0.46. You believe that at your university the proportion is actually less than 0.46. The hypotheses for this scenario are Null Hypothesis: p ≥ 0.46, Alternative Hypothesis: p < 0.46. You conduct a random sample and run a hypothesis test yielding a p-value of 0.2017. What is the appropriate conclusion? Conclude at the 5% level of significance.

Question 15 options:

	1) We did not find enough evidence to say a significant difference exists between the proportion of students that use a MacBook as their primary computer and 0.46
	2) The proportion of students that use a MacBook as their primary computer is greater than or equal to 0.46.
	3) The proportion of students that use a MacBook as their primary computer is significantly less than 0.46.
	4) We did not find enough evidence to say the proportion of students that use a MacBook as their primary computer is larger than 0.46.
	5) We did not find enough evidence to say the proportion of students that use a MacBook as their primary computer is less than 0.46.

Does the amount of hazardous material absorbed by the bodies of hazardous waste workers depend on gender? The level of lead in the blood was determined for a sample of men and a sample of women who dispose of hazardous waste as a full time job. You want to test the hypotheses that the amount absorbed by men is greater than the amount absorbed by women. After performing a hypothesis test for two independent samples, you see a p-value of 0.3307. Of the following, which is the appropriate conclusion?

Question 14 options:

	1) The average amount of lead absorbed by men is significantly greater than the average amount of lead absorbed by women.
	2) We did not find enough evidence to say the average amount of lead absorbed by men is greater than the average amount of lead absorbed by women.
	3) The average amount of lead absorbed by men is less than or equal to the average amount of lead absorbed by women.
	4) We did not find enough evidence to say a significant difference exists between the average amount of lead absorbed by men and the average amount of lead absorbed by women.
	5) We did not find enough evidence to say the average amount of lead absorbed by men is less than the average amount of lead absorbed by women.

Suppose the national average dollar amount for an automobile insurance claim is $745.252. You work for an agency in Michigan and you are interested in whether or not the state average is greater than the national average. The hypotheses for this scenario are as follows: Null Hypothesis: μ ≤ 745.252, Alternative Hypothesis: μ > 745.252. A random sample of 100 claims shows an average amount of $757.836 with a standard deviation of $86.2777. What is the test statistic and p-value for this test?

Question 13 options:

	1) Test Statistic: 1.459, P-Value: 0.0739
	2) Test Statistic: 1.459, P-Value: 0.9261
	3) Test Statistic: -1.459, P-Value: 0.0739
	4) Test Statistic: 1.459, P-Value: 0.1478
	5) Test Statistic: -1.459, P-Value: 0.9261

Answer 1

1.
If the true average fuel economy today is 39.2 MPG which is greater than 24.6 MPG and thus the null hypothesis is rejected is correct decision made.

4) No error has occurred.

2.
Since p-value of 0.2017 is greater than the significance level, the appropriate conclusion is fail to reject the null hypothesis.

5) We did not find enough evidence to say the proportion of students that use a MacBook as their primary computer is less than 0.46.

3.
Since p-value of 0.3307 is greater than the significance level, the appropriate conclusion is fail to reject the null hypothesis.

2) We did not find enough evidence to say the average amount of lead absorbed by men is greater than the average amount of lead absorbed by women.

4.
Standard error of mean , SE = 86.2777 / sqrt(10) = 8.62777

Test statistic = (757.836 - 745.252) / 8.62777 = 1.459

Degree of freedom = n-1 = 100-1 = 99

p-value = P(t > 1.459) = 0.0739

1) Test Statistic: 1.459, P-Value: 0.0739