Tsuko Johnson

2022-05-10

The manufacturer of a certain foreign car sold in the United States claims that it will average 35 miles per gallon of gasoline with the standard deviation of 9.3 miles. To test this claim, a consumer's group randomly selects 40 of these cars and drives them under normal driving conditions. These cars average 28 miles to the gallon. Does this sample indicate that average mileage is more than 35?

nick1337

Expert2022-08-10Added 777 answers

Given that: $n=40$

$\overline{x}=28$

$\sigma =9.3$

To test the hypothesis,

${H}_{0}:\mu =35$

${H}_{a}:\mu 35$

Test statises,

$Z=\frac{\overline{)x}-\mu}{{\displaystyle \raisebox{1ex}{$\sigma $}\!\left/ \!\raisebox{-1ex}{$\sqrt{n}$}\right.}}=\frac{28-35}{{\displaystyle \raisebox{1ex}{$9.3$}\!\left/ \!\raisebox{-1ex}{$\sqrt{40}$}\right.}}$

$=\frac{-7}{1.4705}$

$z=-4.76$

P.value $=0.00001$

Close to 0

Test is significent

TRUE

To test the hypothesis

${H}_{0}:\mu =35$

${H}_{a}:\mu 35$

p-value is less than 0.0001

Test is significant

True!

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