Question 744:

Asked on June 6, 2009

Tags: 1-sample t-test

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1. Q744_1_q7441-samplet.xls

The explanations are below and see the attached excel file for the computations.

a. The Null Hypothesis is that the average miles per gallon is 30. Ho: μ = 30

The alternative Hypothesis is that the average miles per gallon is NOT equal to 30. Ha: μ ≠ 30

b. The mean miles per gallon for the 25 values is 28.172. The sample variance (the sum of the squared deviations from the mean) is 9.206 and the standard deviation is just the square root of the variance = 3.0339

c. We can conduct a 1-sample t-test against the test mean of 30. The 1-sample t-test has the test statistic t* which is found as the difference between the sample mean and test mean divided by the standard error of the mean (SE).

First the difference is 28.172-30 = -1.828. The SE is calculate as the standard deviation divided by the square root of the sample size = 3.033/SQRT(25) = 3.033/5 = .60678.  So our test statistic is -1.828/.60678 = -3.012615.  We can lookup this value in a t-table on 24 degrees of freedom and we get the 2-tailed p-value of .00602.  Since the p-value from the test statistic is below the alpha of .05 we reject the Null Hypothesis and conclude the average miles per gallon IS different than 30. In other words, this data contradicts the claim made by the company since the average is less than 30.