The environmental Protection Agency (EPA) estimated that the 1994 Polaris automo

Question

The environmental Protection Agency (EPA) estimated that the 1994 Polaris
automobile obtains a mean of 35 miles per gallon (mpg) on the highway. However, the
company that manufactures the car claims that the EPA has underestimated the Polaris’
mileage. To support its assertion, the company selects 50 1994 Polaris cars and records the
mileage obtained for each car over a driving course similar to the one used by the EPA. From
the sample, the mean was 38.2 mpg and the standard deviation is 7.1 mpg. State the correct
null and alternative hypotheses that the company wishes to test. Provide and calculate the
test statistic that would be used for conducting the desired test. Using = .025 find the
rejection region for this test. State the conclusion for this test. Find the p-value
of this test.

Explanation / Answer

here null hypothesis: Ho:mean =35

alternate hypothesis: Ha: mean >35

std error of mean =std deviation/(n)1/2 =1.004

for 0.025 level ; test statistic critical value =2.0096

for test stat t=(X-mean)/std error =(38.2-35)/2.0096 =1.5924

as test stat t is less then crtiical value ; we fail to reject null hypothesis that mean is 35.

p value for above test stat =0.0589

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