Question

A consumer agency claims that the average fuel mileage of Sedan A exceeds that of Sedan B. To test this claim, a random sample of 17 Sedan A vehicles were tested and the sample mean fuel mileage was found to be 28.25 miles per gallon with a known population standard deviation of 1.30 miles per gallon. A random sample of 14 Sedan B vehicles also were tested and the sample mean fuel mileage was found to be 27.25 miles per gallon with a known population standard deviation of 1.35 miles per gallon. Use a 1% significance level and assume the fuel mileage values for each of the two populations of sedans are normally distributed.

a. Select the correct symbol to replace "?" in the null hypothesis H₀: μ_A − μ_B? 0

	>
	<
	≥
	≤
	=

b. Select the correct symbol to replace "?" in the alternative hypothesis H_a: μ_A − μ_B? 0

	≠
	≤
	>
	≥
	<

c. Compute the value of the test statistic used to test the agency's claim.

Do not round any intermediate calculations. Round your answer to two decimal places. Enter a "−" sign directly before a negative answer.

Test statistic =

d. Determine the critical value used to test the agency's claim.

Enter your critical value to three decimal places. Enter a "−" sign directly before a negative answer.

Critical value =

e.  Compute the p-value for this hypothesis test.

Use your rounded test statistic from Part c. Do not round any other intermediate calculations. Round your final answer to four decimal places.

p-value =

f. Based on the above results, choose the appropriate initial conclusion.

	Reject the null hypothesis.
	Do not reject the null hypothesis.

g. Based on the claim and your initial conclusion, choose the appropriate final conclusion.

	Do not support the consumer agency's claim.
	Support the consumer agency's claim.

Answer 1

using excel>addin>phstat>two sample test

we have

Z Test for Differences in Two Means
Data
Hypothesized Difference	0
Level of Significance	0.01
Population 1 Sample
Sample Size	17
Sample Mean	28.25
Population Standard Deviation	1.3
Population 2 Sample
Sample Size	14
Sample Mean	27.25
Population Standard Deviation	1.35
Intermediate Calculations
Difference in Sample Means	1
Standard Error of the Difference in Means	0.4792
Z Test Statistic	2.0870
Upper-Tail Test
Upper Critical Value	2.3263
p-Value	0.0184
Do not reject the null hypothesis

=a. the null hypothesis H0: μA − μB =0

b in the alternative hypothesis Ha: μA − μB >0

>

c.the value of the test statistic is

Test statistic =2.09

d. the critical value used to test the agency's claim is 1.645

Critical value = 1.645

e.   the p-value for this hypothesis test.

p-value =0.0184

f. Decision

	Do not reject the null hypothesis.

g. the appropriate final conclusion.

	Do not support the consumer agency's claim.