Question

An automobile manufacturer claims that their van has a 45.9 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the MPG for this van. After testing 11 vans they found a mean MPG of 45.7 with a variance of 2.89. Is there sufficient evidence at the 0.025 level that the vans underperform 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

Step 5 of 5: Make the decision to reject or fail to reject the null hypothesis.

Answer 1

Solution :

Given that ,

= 45.9

= 45.7

n = 11

² = 2.89

= 2.89 = 1.7

1.The null and alternative hypothesis is ,

H₀ :   = 45.9

H_a : <  45.9

2. This is the left tailed test .

Test statistic = z

= ( - ) / / n

= ( 45.7 - 45.9 ) / 1.7 / 11

= -0.39

3. The test statistic = -0.39

= 0.025

Z = Z_0.025 = -1.960

4. Reject Ho if Z < -1.960

The critical value = -1.960

-0.390 > -1.960

Test statistic > Critical value

5. Fail to reject the null hypothesis.