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A car company says that the mean gas mileage for its luxury sedan is at least 21 miles per gallon​ (mpg). You believe the claim is incorrect and find that a random sample of 8 cars has a mean gas mileage of 19 mpg and a standard deviation of 3 mpg. At α=0.025​, test the​ company's claim. Assume the population is normally distributed. State the appropriate hypotheses to test.

User Spittal
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1 Answer

2 votes

Answer:

Null Hypothesis,
H_0 :
\mu \geq 21 miles per gallon​

Alternate Hypothesis,
H_A :
\mu < 21 miles per gallon

Explanation:

We are given that a car company says that the mean gas mileage for its luxury sedan is at least 21 miles per gallon​ (mpg).

You believe the claim is incorrect and find that a random sample of 8 cars has a mean gas mileage of 19 mpg and a standard deviation of 3 mpg.

Let
\mu = mean gas mileage for its luxury sedan

So, Null Hypothesis,
H_0 :
\mu \geq 21 miles per gallon​

Alternate Hypothesis,
H_A :
\mu < 21 miles per gallon​

Here, null hypothesis states that the mean gas mileage for its luxury sedan is at least 21 miles per gallon​ (mpg).

On the other hand, alternate hypothesis states that the mean gas mileage for its luxury sedan is less than 21 miles per gallon​ (mpg).

The test statistics that would be used here is One-sample t test statistics as we don't know about population standard deviation i.e;

T.S. =
(\bar X-\mu)/((s)/(√(n) ) ) ~
t_n_-_1

Hence, the above hypothesis is appropriate for the given situation.

User Yokissa
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