3. Sup pose that an automobile manufacturer advertises that mean gas mileage of

Question

3. Sup pose that an automobile manufacturer advertises that mean gas mileage of 45 miles per gallon. You take a simple ra n 36 hybrid vehicles and test mileage. average is gallon. its new hybrid car has a their gas mileage. You find that in this sample, the equal to 35 miles per gallon with a standard deviation of s = 6 miles per a, write a null hypothesis to be tested at the = .05 level of significance. b. Write an alternative hypothesis to be tested. c. Compute a test statistic. d. Write a decision rule.

Explanation / Answer

Solution: The solution to this problem takes four steps: (1) state the hypotheses, (2) formulate an analysis plan, (3) analyze sample data, and (4) interpret results. We work through those steps below:

Null hypothesis: = 45

Alternative hypothesis: 45

SE = s / sqrt(n) = 6 / sqrt(36) = 6/6 = 1

DF = n - 1 = 6 - 1 = 5

t = (x - ) / SE = (35 - 45)/1 = -10

where s is the standard deviation of the sample, x is the sample mean, is the hypothesized population mean, and n is the sample size.

Since we have a two-tailed test, the P-value is the probability that the t statistic having 5 degrees of freedom is less than -10 or greater than 10.

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