The Bureau of Transportation Statistics reports that the mean cost of Operating

Question

The Bureau of Transportation Statistics reports that the mean cost of Operating an automobile in the United States is 5 9 cents per mile Suppose that a sample taken this year of 100 automobiles shows a mean operating cost of 6.2 cents per mile, and assume that the population standard deviation is 1 5 cents per mile a) Is it appropriate to apply the z-test ? Why or why not? Explain//See the hint at the bottom//b) We have a sample mean that n greater than the mean in the null hypothesis Is not this enough by itself to reject the null hypothesis? Explain why or why not.//Since we are not given a significance level a. we are not able to determine whether this difference is significant enough to reject the null hypothesis//c) How many standard deviations of the mean is 6.2 cents per year? Do you think this is extreme" Explain//Compute the difference and divide by standard deviation//d) Test whether the populations mean coil is less than 5 9 cents per mile. using level of significance or =005 (Clearly state all four steps Explain)

Explanation / Answer

a) Since the population standard deviation is given and sample size is greater than 30 ,it is appropriate to apply z-test.

b) Since we are given a sample of 100 automobiles, we cannot make assumption about the population based on sample parameters. We need to perform statistical test to perform hypothesis test to either reject th hypothesis based on sample data.

c) z = (x-mu)/sigma

=(6.2-5.9)/1.5

= 0.2

We cannot conclude whether this is extreme or not.

d)

One-Sample Z

Test of mu = 5.9 vs < 5.9
The assumed standard deviation = 1.5

95%
Upper
N Mean SE Mean Bound Z P
100 6.20000 0.15000 6.44673 2.00 0.977

Since p value is greater than 0.05 we fail to reject null hypothesis and conclude that the population mean cost is less than 5.9 cents per mile.

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