Question

This problem has 6 parts. This is part 1 of 6.

A car magazine makes the claim, "On average, there is no difference in gas mileage between automatic and manual transmission cars."

The gas mileage in miles per gallon (mpg) for 30 different cars was recorded for both types of transmissions. A summary of the data is given below.

Using this summary data, test the car magazine's claim using a significance level of 0.05.

1. Select the pair of hypotheses that are appropriate for testing this claim.

		H0: µd = 0 (claim) H1: µd > 0
		H0: µd = 0 H1: µd ≠ 0 (claim)
		H0: µd = 0 (claim) H1: µd ≠ 0
		H0: µd ≠ 0 H1: µd = 0 (claim)
		H0: µd = 0 H1: µd > 0 (claim)
		H0: µd ≠ 0 (claim) H1: µd = 0
		H0: µd = 0 H1: µd < 0 (claim)
		H0: µd = 0 (claim) H1: µd < 0

2. Select the choice that best describes the nature and direction of a hypothesis test for this claim.

		This is a left-tail t-test for µd.
		This is a right-tail z-test for µd.
		This is a right-tail t-test for µd.
		This is a two-tail t-test for µd.
		This is a left-tail z-test for µd.
		This is a two-tail z-test for µd.

3. Find the standardized test statistic for this hypothesis test. Round your answer to 2 decimal places.

4. Find the P-value for this hypothesis test. Round your answer to 4 decimal places.

5. Using your previous calculations, select the correct decision for this hypothesis test.

6. Consider the following statements related to the car magazine's claim. Based on the results of your hypothesis test, which of these statements is true? Select the best choice.

Answer 1

1)
Note "On average, there is no difference in gas mileage between automatic and manual transmission cars."

null hypothesis is claim

H0: µd = 0 (claim)
H1: µd ≠ 0

2)
  
note the inequality, it is not directional
This is a two-tail t-test for µd.

3)
Data is not provided
TS= (Xbar )/(s/sqrt(n))
here Xbar and s are sample mean , sample standard deviation for difference

n = 30 here

you can use Excel also for paired t-test , you can TS ,p-value etc directly

4)
df =n-1 = 29
p-value = 2 P(t > |TS| )
= t.dist.2t(abs(TS) , 29) in Excel}

5)
if p-value < alpha, we reject the null hypothesis
if p-value > alpha, we fail to reject the null hypothesis,