Question

Part A: A USA Today article claims that the proportion of people who believe global warming is a serious issue is 0.6, but given the number of people you've talked to about this same issue, you believe it is less than 0.6. The hypotheses for this test are Null Hypothesis: p ≥ 0.6, Alternative Hypothesis: p < 0.6. You take a random sample and perform a hypothesis test, getting a p-value of 0.0831. What is the appropriate conclusion? Conclude at the 5% level of significance.

Question options:

	1) The proportion of people who believe global warming is a serious issue is significantly less than 0.6.
	2) The proportion of people who believe global warming is a serious issue is greater than or equal to 0.6.
	3) We did not find enough evidence to say the proportion of people who believe global warming is a serious issue is larger than 0.6.
	4) We did not find enough evidence to say a significant difference exists between the proportion of people who believe global warming is a serious issue and 0.6
	5) We did not find enough evidence to say the proportion of people who believe global warming is a serious issue is less than 0.6.

Part B: Consumers Energy states that the average electric bill across the state is $68.76. You want to test the claim that the average bill amount is actually different from $68.76. The hypotheses for this situation are as follows: Null Hypothesis: μ = 68.76, Alternative Hypothesis: μ ≠ 68.76. If the true statewide average bill is $68.76 and the null hypothesis is not rejected, did a type I, type II, or no error occur?

Question options:

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

Part C: Is there a relationship between car purchases and political party? You make a tabulation of people who were asked about the origin of their primary car and their political party affiliation. To determine if Political Party and Car Origin are dependent, what are the appropriate hypotheses?

Question options:

	1) HO: Political Party and Car Origin are not related to each other. HA: Political Party and Car Origin display a positive correlation.
	2) HO: Political Party and Car Origin are not related to one another. HA: Political Party and Car Origin are dependent on each other.
	3) HO: Political Party and Car Origin are independent of one another. HA: Political Party and Car Origin display a negative correlation.
	4) There is not enough information to choose the correct set of hypotheses.
	5) HO: Political Party and Car Origin are related to one another. HA: Political Party and Car Origin are independent of each other.

Part D: Suppose that in a certain neighborhood, the cost of a home is proportional to the size of the home in square feet. If the regression equation quantifying this relationship is found to be (cost) = 87.718*(size) + 629.969, what does the slope indicate?

Question options:

	1) When size increases by 1 square foot, cost increases by 87.718 dollars.
	2) When cost increases by 1 dollar, size increases by 87.718 square feet.
	3) When cost increases by 1 dollar, size increases by 629.969 square feet.
	4) We are not given the dataset, so we cannot make an interpretation.
	5) When size increases by 1 square foot, cost increases by 629.969 dollars.

Answer 1

Solution: Part A: A USA Today article claims that the proportion of people who believe global warming is a serious issue is 0.6, but given the number of people you've talked to about this same issue, you believe it is less than 0.6. The hypotheses for this test are Null Hypothesis: p ≥ 0.6, Alternative Hypothesis: p < 0.6. You take a random sample and perform a hypothesis test, getting a p-value of 0.0831. What is the appropriate conclusion? Conclude at the 5% level of significance.

Answer: 5) We did not find enough evidence to say the proportion of people who believe global warming is a serious issue is less than 0.6.

Because p-value = 0.0831 is greater than the significance level = 0.05, we therefore fail to reject the null hypothesis and conclude that there is not enough evidence to say the proportion of people who believe global warming is a serious issue is less than 0.6

Part B: Consumers Energy states that the average electric bill across the state is $68.76. You want to test the claim that the average bill amount is actually different from $68.76. The hypotheses for this situation are as follows: Null Hypothesis: μ = 68.76, Alternative Hypothesis: μ ≠ 68.76. If the true statewide average bill is $68.76 and the null hypothesis is not rejected, did a type I, type II, or no error occur?

Answer: 1) No error has occured.

Because we have made correct decision, therefore there is no error.

Part C: Is there a relationship between car purchases and political party? You make a tabulation of people who were asked about the origin of their primary car and their political party affiliation. To determine if Political Party and Car Origin are dependent, what are the appropriate hypotheses?

Answer: The correct option is

2) HO: Political Party and Car Origin are not related to one another.
HA: Political Party and Car Origin are dependent on each other.

Part D: Suppose that in a certain neighborhood, the cost of a home is proportional to the size of the home in square feet. If the regression equation quantifying this relationship is found to be (cost) = 87.718*(size) + 629.969, what does the slope indicate?

Answer: 1) When size increases by 1 square foot, cost increases by 87.718 dollars.