Question

It is necessary for an automobile producer to estimate the number of miles per gallon achieved by its cars. Suppose that the sample mean for a random sample of 100 cars is 28.6 miles and assume the standard deviation is 3.9 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 ?=.05 by giving the following:

(a)    positive critical ? score    

(b)    negative critical ? score    

(c)    test statistic    

The final conclustion is

A. There is not sufficient evidence to reject the null hypothesis that ?=27.
B. We can reject the null hypothesis that ?=27 and accept that ?≠27

Answer 1

H0: = 27

Ha: 27

This is two tailed test.

a)

Positive z-score (critical value) = 1.96

b)

negative z-score (critical value) = -1.96

c)

Test statistics

z = ( - ) / ( / sqrt(n) )

= ( 28.6 - 27) / ( 3.9 / sqrt(100) )

= 4.10

Since Test statistics > 1.96 , Reject H0.

Conclusion = We can reject the null hypothesis that = 27 and accept that 27