Suppose that you are working for an automobile manufacturer and you want to stat

Question

Suppose that you are working for an automobile manufacturer and you want to statistically estimate the gas mileage of a new car model, based on the few that are available. To accomplish this, you are provided with nine vehicles from a much larger total population produced for which you achieved the following results. a. Find the average and standard deviation of the sample set b. Find the 95% confidence interval based on these samples c. Your company wants to claim that the mileage is 26.0 or higher at a confidence level of 95%. Is the hypothesis justified?

Explanation / Answer

a) mean = 23 , standard deviation = 2.121

b) t value at 95% CI = 2.306

CI = mean + / - t * ( s /sqrt(n))

= 23 + /- 2.306 * ( 2.121 / sqrt(9))

= (21.369 , 24.630)

c)

H0 : mu = 26

Ha : mu >26

test statistic:

t = ( x - mu ) / (s / sqrt(n))

= ( 23 -26) / ( 2.121/sqrt(9))

= -4.24

Now, we need to find p value using t = -4.24 , df = 8

p value = .001419.

As p value is less than 0.05 so we reject the null hypothesis

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