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 14 Sedan A vehicles were tested and the sample mean fuel mileage was found to be 25.30 miles per gallon with a known population standard deviation of 1.45 miles per gallon. A random sample of 17 Sedan B vehicles also were tested and the sample mean fuel mileage was found to be 24.10 miles per gallon with a known population standard deviation of 1.90 miles per gallon. Use a 10% 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.

	Do not reject the null hypothesis.
	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

a)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ1 <= μ2

b)

Alternative Hypothesis, Ha: μ1 > μ2

c)

Pooled Variance
sp = sqrt(s1^2/n1 + s2^2/n2)
sp = sqrt(2.1025/14 + 3.61/17)
sp = 0.6021

Test statistic,
z = (x1bar - x2bar)/sp
z = (25.3 - 24.1)/0.6021
z = 1.99

d)
Rejection Region
This is right tailed test, for α = 0.1
Critical value of z is 1.282.
Hence reject H0 if z > 1.282
e)

P-value Approach
P-value = 0.0233

f)

As P-value < 0.1, reject the null hypothesis.

g)
Support the consumer agency's claim.