Question

The federal government recently granted funds for a special program designed to reduce crime in high-crime areas. A study of the results of the program in high-crime areas of Miami, Florida, are being examined to test the effectiveness of the program. The difference in crimes reported is calculated as (crimes after - crimes before). You want to test whether the average number of crimes reported after are different from the average number of crimes reported before. What are the hypotheses for this test?

Question 10 options:

	1) HO: μD ≠ 0 HA: μD = 0
	2) HO: μD ≥ 0 HA: μD < 0
	3) HO: μD ≤ 0 HA: μD > 0
	4) HO: μD = 0 HA: μD ≠ 0
	5) HO: μD > 0 HA: μD ≤ 0

Question 11 (1 point)

Will eating oatmeal promote healthy levels of cholesterol? A consumer reports analyst took a sample of 39 people with high cholesterol and asked them to eat oatmeal once a day for 3 months. Measurements were taken of their cholesterol levels before and after the 3 months in mg/dl. The analyst is testing whether the cholesterol levels after the diet are different from the cholesterol levels before the diet. The hypotheses for this test are as follows: Null Hypothesis: μ_D = 0, Alternative Hypothesis: μ_D ≠ 0. If the analyst calculated the mean difference in cholesterol levels (after - before) to be 0.69 mg/dL with a standard deviation of 5.06 md/dL, what is the test statistic and p-value for the paired hypothesis t-test?

Question 11 options:

	1) Test Statistic: 0.852, P-Value: 1.8
	2) Test Statistic: -0.852, P-Value: 0.4
	3) Test Statistic: 0.852, P-Value: 0.4
	4) Test Statistic: 0.852, P-Value: 0.2
	5) Test Statistic: 0.852, P-Value: 0.8

Question 12 (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 0.8488 in the paired samples t-test, what is the appropriate conclusion?

Question 12 options:

	1) 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.
	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 significantly larger than 0. The average gas mileage was higher with the additive.
	4) The average difference in gas mileage is less than or equal to 0.
	5) 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.

Question 13 (1 point)

Suppose the national average dollar amount for an automobile insurance claim is $795.62. 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 ≤ 795.62, Alternative Hypothesis: μ > 795.62. Suppose the true state average is $920.27 and the null hypothesis is not rejected, did a type I, type II, or no error occur?

Question 13 options:

	1) Type II 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 I Error has occurred

Question 14 (1 point)

Consumers Energy states that the average electric bill across the state is $48.63. You want to test the claim that the average bill amount is actually different from $48.63. The hypotheses for this situation are as follows: Null Hypothesis: μ = 48.63, Alternative Hypothesis: μ ≠ 48.63. If the true statewide average bill is $48.63 and the null hypothesis is rejected, did a type I, type II, or no error occur?

Question 14 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.

Answer 1

## Question 10 )

The federal government recently granted funds for a special program designed to reduce crime in high-crime areas. A study of the results of the program in high-crime areas of Miami, Florida, are being examined to test the effectiveness of the program. The difference in crimes reported is calculated as (crimes after - crimes before).

claim : You want to test whether the average number of crimes reported after are different from the average number of crimes reported before. What are the hypotheses for this test?

Answer : option (4) is correct : Ho : μD = 0 vs H1 : μD ≠ 0

## Question 11 )

Will eating oatmeal promote healthy levels of cholesterol? A consumer reports analyst took a sample of 39 people with high cholesterol and asked them to eat oatmeal once a day for 3 months. Measurements were taken of their cholesterol levels before and after the 3 months in mg/dl. The analyst is testing whether the cholesterol levels after the diet are different from the cholesterol levels before the diet. The hypotheses for this test are as follows: Null Hypothesis: μD = 0, Alternative Hypothesis: μD ≠ 0.

If the analyst calculated the mean difference in cholesterol levels (after - before) to be 0.69 mg/dL with a standard deviation of 5.06 md/dL, what is the test statistic and p-value for the paired hypothesis t-test?

Answer : t = mean difference / √ (variance / n )

t = 0.69 / ( √ 5.06^2 / 39)

t = 0.852 and p value is 0.40

correct option is : 3 : test statistics value is 0.852 and p value is 0.40

##  Question 12 (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: μD ≤ 0, Alternative Hypothesis: μD > 0. If they calculate a p-value of 0.8488 in the paired samples t-test, what is the appropriate conclusion?

Answer : correct option is 1 ) we did not find enough evidence to say there was a significnatly positve average difference in gas milleage The additive does not appear to be effective .

##  Question 13 (1 point)

Suppose the national average dollar amount for an automobile insurance claim is $795.62. 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 ≤ 795.62, Alternative Hypothesis: μ > 795.62. Suppose the true state average is $920.27 and the null hypothesis is not rejected, did a type I, type II, or no error occur?

Answer : type I error is we rejecct Ho when it is true

and type II erroe is we fail to reject Ho when it is false

here the null hypothesis is not rejected here type II error occur .

correct option is ( 1 ) Type II Error has occured

## Question 14 (1 point)

Consumers Energy states that the average electric bill across the state is $48.63. You want to test the claim that the average bill amount is actually different from $48.63. The hypotheses for this situation are as follows: Null Hypothesis: μ = 48.63, Alternative Hypothesis: μ ≠ 48.63. If the true statewide average bill is $48.63 and the null hypothesis is rejected, did a type I, type II, or no error occur?

Answer : here null hypothesis is rejected hence here type I error occur

correct option is (5) Type I error has occurred .