Question

An automobile manufacturer claims that its van has a 39.0 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the MPG for this van since it is believed that the van has an incorrect manufacturer's MPG rating. After testing 120 vans, they found a mean MPG of 38.8. Assume the standard deviation is known to be 2.2. A level of significance of 0.02 will be used.

1. State hypothesis. H0 and H1.2. Determine the value of the level of significance.3. Find the value of the test statistic. 4. Specify if the test is one tailed or two tailed.5. Find the P-value of the test statistic. 6. Determine the conclusion.

Answer 1

(1) H0: The mean MPG rating of the vans is 38.8

H1: The mean MPG rating of the vans is not 38.8

(2) The significance level is 2%

(3) The test statistic is -1

(4) The test is two tailed

(5) Fail to reject H0. The mean MPG rating of the vans is 38.8

Explanation:

(1) A null hypothesis is a statement from a population parameter which is either rejected or accepted (fail to reject) upon testing.

An alternate hypothesis is also a statement from the population parameter that negates the null hypothesis and is accepted if the null hypothesis is rejected.

(2) The level of significance is 0.02 (2%)

(3) Z = (sample mean - population mean) ÷ sd/√n

sample mean = 38.8, population mean = 39, sd = 2.2, n = 120

Z = (38.8 - 39) ÷ 2.2/√120 = -0.2 ÷ 0.2 = -1

(4) A two tailed test is identified by the inequality not equal to.

(5) P-value = 1 - cumulative area of the test statistic = 1 - 0.8413 = 0.1587

(6) Fail to reject H0 because the P-value (0.1587) is greater than the significance level (0.02).