Question

(1 point) 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 50 cars is 30.2 mpg and assume the standard deviation is 2.8 mpg. Now suppose the car producer wants to test the hypothesis that μ, the mean number of miles per gallon, is 29.9 against the alternative hypothesis that it is not 29.9. Conduct a test using a significance level of α=.05 by giving the following:

(a) The test statistic (30.2-29.9)/(2.8/sqrt50)

(b) The P -value___

(c) The final conclusion is

A. There is not sufficient evidence to reject the null hypothesis that μ=29.9.

B. We can reject the null hypothesis that μ=29.9 and accept that μ≠29.9.

Answer 1

The hypotheses are

Here the sample size is and sample mean , sample standard deviation .

Since the population standard deviation is not known, we use t-distribution.

a)The test statistics is

b)The P-value is

c)Since the P-value is greater than significance level, we accept the null hypothesis.

A. There is not sufficient evidence to reject the null hypothesis that μ=29.9.