Question

1 point) 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 100100 cars is 28.228.2 miles and assume the standard deviation is 3.23.2 miles. Now suppose the car producer wants to test the hypothesis that μμ, the mean number of miles per gallon, is 29.829.8 against the alternative hypothesis that it is not 29.829.8. Conduct a test using α=.05α=.05 by giving the following:

(a)    positive critical zz score    

(b)    negative critical zz score    

(c)    test statistic    

The final conclustion is

A. We can reject the null hypothesis that μ=29.8μ=29.8 and accept that μ≠29.8μ≠29.8.
B. There is not sufficient evidence to reject the null hypothesis that μ=29.8μ=29.8.

Answer 1

1)

Solution :

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :   = 29.8

H_a : 29.8

= 28.2

= 100

= 3.2

n = 100

Test statistic = z = ( - ) / / n = (28.2 - 29.8) / 3.2 / 100 = -5

This is the right tailed test .

P(z < -5) = 0

P-value = 2 * 0 = 0

= 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

Positive z value = +1.96

Negative z value = -1.96

Reject the null hypothesis .

Test statistc < critical value

B. There is not sufficient evidence to reject the null hypothesis that μ=29.8