Question

An automobile manufacturer has given its jeep a 31.4 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the actual MPG for this jeep since it is believed that the jeep performs under the manufacturer's MPG rating. After testing 110 jeeps, they found a mean MPG of 31.6. Assume the population standard deviation is known to be 1.9. Is there sufficient evidence at the 0.02 level to support the testing firm's claim?

Step 1 of 6: State the null and alternative hypotheses.

Step 2 of 6: Find the value of the test statistic. Round your answer to two decimal places.

Step 3 of 6: Specify if the test is one-tailed or two-tailed.

Step 4 of 6: Find the P-value of the test statistic. Round your answer to four decimal places.

Step 5 of 6: Identify the level of significance for the hypothesis test

Step 6 of 6: Make the decision to reject or fail to reject the null hypothesis.

Answer #1

1)

H0: 31.4

Ha: > 31.4

2)

Test statistics

z = ( - ) / ( / sqrt(n) )

= (31.6 - 31.4) / (1.9 / sqrt(110) )

= **1.10**

3)

This is **one tailed** test.

4)

p-value = P(Z > z)

= P(Z > 1.10)

= **0.1357**

5)

Level of significance = **0.02**

6)

Since p-value > 0.02 level, **Fail to reject
H0**

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