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t is necessary for an automobile producer to estimate the number of miles per ga

ID: 3072947 • Letter: T

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 , the mean number of miles per gallon, is 30.5 against the alternative hypothesis that it is not 30.5. Conduct a test using =.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 =30.5.

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

Explanation / Answer

The statistical software output for this problem is:

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

Hypothesis test results:

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 =30.5. Option A is correct.

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