A car company says that the mean gas milage for its luxurysadan ia at least 22 m

Question

A car company says that the mean gas milage for its luxurysadan ia at least 22 miles. You believe the claim is incorrect and find a random sample of 8 cars has amean gas mileage of 21 mpg and a standard deviation of 4 mpg. At a=0.10, test the companys claim. Assume the population is normally distributed.

What is the value of the standard test statistic?

The standardized test statistic is         (round to two decimal places as needed)

What is the critical value          (round to three decimal places as needed)

What is the outcome and the conclusion of this test?

Please give detail steps on how you arrived at the answers please, having a hard time following the book, the examples are not very clear sometimes. Thank you

Explanation / Answer

Ho= u=22

Ha= u<22

a) here the test static to be found = (x-mean)/(standard deviation/sqrt(n))

now the x = 21

mean = 22

test static = (21-22)/(4/sqrt(8)) = -0.7092

b) the standardised test static = -0.71

c) the critical value or the p value will be taen from the t table with t static = -0.71

and degree of freedom = 8-1 = 7

now the p vales comes out to be = 0.2503

d) the result is not significant for p <0.10

therefore we will reject the null hypothesis.

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