Question

Please state the step number next to the answers given, thank you!

An automobile manufacturer claims that their jeep has a 31.9 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the MPG for this jeep. After testing 16 jeeps they found a mean MPG of 32.1 with a standard deviation of 1.6. Is there sufficient evidence at the 0.05 level that the jeeps outperform the manufacturer's MPG rating? Assume the population distribution is approximately normal.

Step 1 of 5: State the null and alternative hypotheses.
Step 2 of 5: Find the value of the test statistic. Round your answer to three decimal places.
Step 3 of 5: Specify if the test is one-tailed or two-tailed.
Step 4 of 5: Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places. (Reject H0 if t>_______)
Step 5 of 5: Make the decision to reject or fail to reject the null hypothesis.

Answer 1

Solution :

= 31.9

=32.1

s =1.6

n = 16

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :    = 31.9

H_a :     31.9

Test statistic = z

= ( - ) / s / n

= (32.1-31.9 ) / 1.6 / 16

= 0.500

Test statistic = t = 0.500

P-value = 0.6171

= 0.05  

P-value ≥

0.6243 ≥ 0.05

It is observed that ∣t∣=0.5 ≤ t_c​=2.131, it is then concluded that the null hypothesis is not rejected

Fail to reject the null hypothesis .

There is insufficient evidence to suggest that