Question

Consumers Energy states that the average electric bill across the state is $41.553. You want to test the claim that the average bill amount is actually greater than $41.553. The hypotheses for this situation are as follows: Null Hypothesis: μ ≤ 41.553, Alternative Hypothesis: μ > 41.553. A random sample of 47 customer's bills shows an average cost of $43.307 with a standard deviation of $8.0202. What is the test statistic and p-value for this test?

	1) Test Statistic: -1.499, P-Value: 0.9297
	2) Test Statistic: 1.499, P-Value: 0.0703
	3) Test Statistic: 1.499, P-Value: 0.1406
	4) Test Statistic: 1.499, P-Value: 0.9297
	5) Test Statistic: -1.499, P-Value: 0.0703

It is reported in USA Today that the average flight cost nationwide is $396.81. You have never paid close to that amount and you want to perform a hypothesis test that the true average is actually less than $396.81. The hypotheses for this situation are as follows: Null Hypothesis: μ ≥ 396.81, Alternative Hypothesis: μ < 396.81. A random sample of 32 flights shows an average cost of $407.477 with a standard deviation of $59.2227. What is the test statistic and p-value for this test?

	1) Test Statistic: 1.019, P-Value: 1.6838
	2) Test Statistic: -1.019, P-Value: 0.1581
	3) Test Statistic: -1.019, P-Value: 0.8419
	4) Test Statistic: 1.019, P-Value: 0.1581
	5) Test Statistic: 1.019, P-Value: 0.8419

Suppose the national average dollar amount for an automobile insurance claim is $973.04. 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 ≤ 973.04, Alternative Hypothesis: μ > 973.04. You take a random sample of claims and calculate a p-value of 0.3431 based on the data, what is the appropriate conclusion? Conclude at the 5% level of significance.

	1) The true average claim amount is significantly higher than $973.04.
	2) We did not find enough evidence to say a significant difference exists between the true average claim amount and $973.04.
	3) The true average claim amount is less than or equal to $973.04.
	4) We did not find enough evidence to say the true average claim amount is higher than $973.04.
	5) We did not find enough evidence to say the true average claim amount is less than $973.04.

Suppose the national average dollar amount for an automobile insurance claim is $823.38. 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 ≤ 823.38, Alternative Hypothesis: μ > 823.38. You take a random sample of claims and calculate a p-value of 0.0177 based on the data, what is the appropriate conclusion? Conclude at the 5% level of significance.

	1) We did not find enough evidence to say the true average claim amount is higher than $823.38.
	2) The true average claim amount is significantly different from $823.38.
	3) The true average claim amount is significantly higher than $823.38.
	4) The true average claim amount is less than or equal to $823.38.
	5) The true average claim amount is significantly less than $823.38.

Answer 1

(a) right choice is (2) Test Statistic: 1.499, P-Value: 0.0703

test statistic t==(43.307-41.553)/(8.0202/sqrt(47))=1.499 with n-1=47-1=46 df
p-value=P(t>1.499)=0.0703 ( using ms-excel=tdist(1.499,46,1))

this is right tailed test so p-value is one tailed

(b) right choice is (4)Test Statistic: 1.019, P-Value: 0.8419

test statistic t==(407.477-396.81)/(59.2227/sqrt(32))=1.019 with n-1=32-1=31 df
p-value=P(t<1.019)=0.8419

(c) right choice is (5) We did not find enough evidence to say the true average claim amount is higher than $973.04.

since the p-value=0.3431 is more than alpha=0.05, so we fail to reject null hypothesis and conclude that  national average dollar amount for an automobile insurance claim is μ ≤ 973.04 ( or not greater than  $973.04 )

(d) right choice is (3)The true average claim amount is significantly higher than $823.38.

since the p-value=0.0177 is less than alpha=0.05, so we reject null hypothesis in favor of alternate hypothesis Ha: μ > 823.38 and conclude that  true average claim amount is significantly higher than $823.38