(1 point) It is necessary for an automobile producer to estimate the number of m

Question

(1 point) 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 100 cars is 27 miles and assume the standard deviation is 2.6 miles. Now suppose the car producer wants to test the hypothesis that , the mean number of miles per gallon, is 24.4 against the alternative hypothesis that it is not 24.4. 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. We can reject the null hypothesis that =24.4 and accept that 24.4.
B. There is not sufficient evidence to reject the null hypothesis that =24.4.

Explanation / Answer

Solution:

Here, we have to use the one sample z test for the population mean.

The null and alternative hypothesis for this test is given as below:

Null hypothesis: H0: The mean number of miles per gallon is 24.4.

Alternative hypothesis: Ha: The mean number of miles per gallon is not 24.4.

H0: µ = 24.4 versus Ha: µ 24.4

This is a two tailed test.

The test statistic formula is given as below:

Z = (Xbar - µ) / [ /sqrt(n)]

We are given

Sample mean = Xbar = 27

Population standard deviation = = 2.6

Sample size = n = 100

Population mean = µ = 24.4

Level of significance = = 0.05

Positive critical value = 1.96

Negative critical value = -1.96

Z = (27 – 24.4) / [2.6/sqrt(100)]

Z = 10

P-value = 0.00

= 0.05

P-value < = 0.05

So, we reject the null hypothesis

The final conclusion is

A. We can reject the null hypothesis that =24.4 and accept that 24.4.

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