It is necessary for an automobile producer to estimate the number of miles per gallon achieved by its cars. Suppose that the sample mean for a random sample of 100 cars is 27.2 miles and assume the standard deviation is 2.4 miles. Now suppose the car producer wants to test the hypothesis that μ, the mean number of miles per gallon, is 25.9 against the alternative hypothesis that it is not 25.9. Conduct a test using α=.05 by giving the following:

Step-by-step explanation:

Given that the sample mean for a random sample of 100 cars is 27.2 miles and assume the standard deviation is 2.4 miles.

H0: x bar = 25.9

Ha: x bar ≠ 25.9

(Two tailed test at 95% confidence)

Alpha = 0.05

The hypothetical mean is 25.900

The actual mean is 27.200

The difference between these two values is 1.300

The 95% confidence interval of this difference:

From - 3.462 to 6.062

t = 0.5417

df = 99

standard error of difference = 2.400

The two-tailed P value equals 0.5893

Since p >0.05 this difference is considered to be not statistically significant.