Question

It is necessary for an automobile producer to estimate the number of miles per gallon (mpg) achieved by its cars. Suppose that the sample mean for a random sample of 5050 cars is 30.630.6 mpg and assume the standard deviation is 3.63.6 mpg. Now suppose the car producer wants to test the hypothesis that μμ, the mean number of miles per gallon, is 31.631.6 against the alternative hypothesis that it is not 31.631.6. Conduct a test using a significance level of α=.05α=.05 by giving the following:

(a) The test statistic (give to 3 decimal places) is

(b) The P -value (give to 4 decimal places) is

(c) The final conclusion is

A. We can reject the null hypothesis that μ=31.6μ=31.6 and accept that μ≠31.6μ≠31.6.
B. There is not sufficient evidence to reject the null hypothesis that μ=31.6μ=31.6.

Answer 1

a)
TS = -1.964
b)
p-value = 0.0495
c)
A) reject

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