4. Moore, 7.23 (modified) Computers in some vehicles calculate various quantities related to performance.One of these is miles per gallon. A person records the following mpg while a Toyota Highlander Hybridis set to 60 mpg with cruise control. Here are the data:37.2 21.0 17.4 24.9 27.0 36.9 38.8 35.3 32.3 23.919.0 26.1 25.8 41.4 34.4 32.5 25.3 26.5 28.2 22.1

(a) What is the sample mean? What is the sample standard deviation? (Hint: USE EXCEL).

(b) Use your answer from part (a) to construct both 90 percent and 95 percent confidence intervalsaround the sample mean.1

(c) Suppose your null hypothesis is that the mean number of miles per gallon is 30 mpg and that youare doing a two-sided hypothesis. Write down the null hypothesis and the alternative.

(d) What is the test-statistic?

(e) Compare your hypothesis to the relevant critical value for the 90, 95, and 99 percent confidencelevels. State your conclusion.