Question

t 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 150 cars is 30.2 miles and assume the standard deviation is 3.6 miles. Now suppose the car producer wants to test the hypothesis that μ, the mean number of miles per gallon, is 30.5 against the alternative hypothesis that it is not 30.5. Conduct a test using α=.05 by giving the following:

(a) positive critical z score:

(b) negative critical z score:

(c) test statistic :

The final conclustion is

A. There is not sufficient evidence to reject the null hypothesis that μ=30.5.

B. We can reject the null hypothesis that μ=30.5 and accept that μ≠30.5.

Answer 1

The statistical software output for this problem is:

One sample Z summary hypothesis test:
μ : Mean of population
H₀ : μ = 30.5
H_A : μ ≠ 30.5
Standard deviation = 3.6

Hypothesis test results:

Mean	n	Sample Mean	Std. Err.	Z-Stat	P-value
μ	150	30.2	0.29393877	-1.0206207	0.3074

Hence,

a) Positive critical z score = 1.96

b) Negative critical z score = -1.96

c) Test statistic = -1.0206

Final conclusion: There is not sufficient evidence to reject the null hypothesis that μ=30.5. Option A is correct.