Question

An automobile manufacturer claims that their leading compact car averages 36 mpg in the city. The population standard deviation is 8 mpg for city driving. Suppose a city police department purchases 64 cars from this auto manufacturer. If these cars were driven exclusively under city conditions and averaged 34 mpg, can one argue that the manufacturer's claim is too high at 5% a. State the null and alternative hypothesis b. Determine and draw the hypothesis test model (Label everything) c. Determine the critical value(s) and test statistic d Determine the conclusion.

Answer 1

(a)

Ho: = 36 (claim)

Ha: < 36

Null hypothesis states that compact car averages 36 mpg in the city.

Alternative hypothesis states that compact car averages less than 36 mpg in the city.

(b) level of significance = 0.05

n = 64

= 8

This is a left tailed test, hence if the z stat is less than z critical (falls in the rejection area) we reject the Null hypothesis.

and if z stat is greater  than z critical,we fail to reject the Ho.

z critical for left tailed test=  - 1.65

(c) Test statistics

z critical for left tailed test=  - 1.65

As the z stat (-2) falls in the rejection region, we reject the Null hypothesis.

(d) Hence we have sufficient evidence to believe that compact car averages less than 36 mpg in the city.