Question

13. (11pt) Automobile manufacturers are very interested in improving the average gas mileage of their newer vehicles. One manufacturer knows that for their hybrid model car, the gas mileages are normally distributed with a mean of 32 mpg. The new model of this car is about to ship out, so the manufacturer randomly selects a sample of 7 new hybrid cars and determines that the mean gas mileage is 29.5 mpg with a standard deviation of 1.32 mpg. Is there significant evidence to conclude that the average gas mileage has decreased at the a = 0.01 level of significance? Use the p-value method, showing all work and steps. Assume all the conditions to conduct the test are met.

Answer 1

Here we have: X = 29.5 S = 1.32 n = 7 a = 0.01 Hypothesis: Hoi u = 32 Hai u < 32 Test statistics: t-distribution (o unknown) X-u t = = 29.5-32 1.32 7 = -5.01 S vn df = n-1 = 7 -1 = 6

P-value = p (t>/-5.011) = 0.0012 Reject the null hypothesis. Conclusion: Here we have sufficient evidence to reject the null hypothesis. P- value is less than alpha value We can support the claim that the average gas millage has decreased