Question

LaTech Stat Ch6: Problem 4 gallon achieved by its cars. Suppose that the sample mean for a randorm sample of 100 cars is 29.7 miles and assume the standard deviation is 3.6 miles. Now suppose the car producer wants to test the hypothesis that , the mean number of miles per gallon, is 27 against the alternative hypothesis that it is not 27. Conduct a test using a 05 by giving the following OA.We can reject the null hypothesis that μ 27 and accept that μ 27 O B. There is not sufficient evidence to reject the null hypothesis that μ = 27

Answer 1

Given that, sample size ( n ) = 100

sample mean = 29.7 miles

population standard deviation = 3.6 miles

The null and alternative hypotheses are,

Ho : μ = 27

Ha 27

crirical values at significance level of 0.05 are, Z^* = ± 1.96

a) positive critical z score = 1.96

b) negative critical z score = -1.96

c) Test statistic is,

29.7- 27 =7.5 100

Test statistic = 7.5

since, Z = 7.5 > 1.96

we can reject the null hypothesis that
μ 27
and accept that
μメ27