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 130130 cars is 28.528.5 miles and assume the standard deviation is 3.13.1 miles. Now suppose the car producer wants to test the hypothesis that ?μ, the mean number of miles per gallon, is 30.830.8 against the alternative hypothesis that it is not 30.830.8. Conduct a test using ?=.05α=.05 by giving the following:

(a)    positive critical ?z score    

(b)    negative critical ?z score    

(c)    test statistic    

The final conclustion is

Answer 1

Solution :

This is the two tailed test,  

The null and alternative hypothesis is ,

H₀ :   = 30.8

H_a :    30.8

= 0.05  

/2 = 0.025

Z_/2 = Z_0.025 = ±1.96

a) positive critical value z-score = 1.96

b) negative critical value z-score = -1.96

c) Test statistic = z

= ( - ) / / n

= (28.5 - 30.8 ) / 3.1 / 130

Test statistic = z = -8.46

Fail to reject null hypothesis, because test statistic is not betweencritical value -1.96 and 1.96