It is necessary for an automobile producer to estimate the number of miles per g

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 120 cars is 28.3 miles and assume the standard deviation is 2.2 Now suppose the car producer wants to test the hypothesis that p. the mean number of per gallon, is 29.1 against the alternative hypothesis that it is not 29. L Conduct a test using alpha = .05 by giving the following ' (a) positive critical z score (b) negative critical z score (c) test statistic The final conclusion is We can reject the null hypothesis that mu = 29.1 and accept that mu notequalto 29.1 There is not sufficient evidence to reject the null hypothesis that mu = 29.1

Explanation / Answer

Solution:

Sample size = 120
With a t-distribution (109 degrees of freedom and alpha =.025):

(a) positive critical score 1.96
(b) negative critical score -1.96

H0: = 29.1
HA: 29.1
Sample mean = 28.3
Standard deviation = 2.2
Standard error of mean = s / n
Standard error of mean = 2.2 / 120
SE = 2.2/10.9545
Standard error of mean 0.2008
t = (xbar- ) / SE
t = (28.3-29.1) / 0.2008
t = -3.9841 ---- test statistic

The final conclusion is
A. We can reject the null hypothesis that = 29.1 and accept that 29.1

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