a car company says that the mean gas mileage for its luxury sedan is at least 25 miles per gallon (mpg). you believe the claim is incorrect and find that a random sample of 5 cars has a mean gas mileage of 23 mpg and a standard deviation of 2 mpg. at $ \alpha = 0.05 $, test the companys claim. assume the population is normally distributed. click here to view the t - distribution table. click here to view page 1 of the normal table. click here to view page 2 of the normal table. state the appropriate hypotheses to test. a. $ h _ { 0 } : \mu \leq 25 $ $ h _ { a } : \mu 25 $ b. $ h _ { 0 } : \mu \ eq 25 $ $ h _ { a } : \mu = 25 $ c. $ h _ { 0 } : \mu \geq 25 $ $ h _ { a } : \mu

Question

a car company says that the mean gas mileage for its luxury sedan is at least 25 miles per gallon (mpg). you believe the claim is incorrect and find that a random sample of 5 cars has a mean gas mileage of 23 mpg and a standard deviation of 2 mpg. at $ \alpha = 0.05 $, test the companys claim. assume the population is normally distributed. click here to view the t - distribution table. click here to view page 1 of the normal table. click here to view page 2 of the normal table. state the appropriate hypotheses to test. a. $ h _ { 0 } : \mu \leq 25 $ $ h _ { a } : \mu > 25 $ b. $ h _ { 0 } : \mu \
eq 25 $ $ h _ { a } : \mu = 25 $ c. $ h _ { 0 } : \mu \geq 25 $ $ h _ { a } : \mu < 25 $ d. $ h _ { 0 } : \mu = 25 $ $ h _ { a } : \mu \
eq 25 $ what is the value of the standardized test statistic? the standardized test statistic is $ - 2.24 $. (round to two decimal places as needed.) what is the critical value? the critical value is $ - 2.132 $. (round to three decimal places as needed.) what is the outcome and the conclusion of this test? $ h _ { 0 } $. at the 5% significance level, there is evidence to the car companys claim that the mean gas mileage for the luxury sedan is at least 25 miles per gallon.

Accepted Answer

# Explanation:
## Step1: Compare test statistic and critical value
We have the standardized test statistic $t=-2.24$ and the critical value $t_{critical}=- 2.132$.
Since $t=-2.24<t_{critical}=-2.132$ (in a left - tailed test).

## Step2: Make a decision about $H_0$
In a hypothesis test, if the test statistic falls in the rejection region (for a left - tailed test, $t < t_{critical}$), we reject the null hypothesis $H_0$.

## Step3: Interpret the result
Rejecting $H_0:\mu\geq25$ means that at the $5\%$ significance level, there is sufficient evidence to reject the car company’s claim that the mean gas mileage for the luxury sedan is at least $25$ miles per gallon.

# Answer:
Reject $H_0$. At the $5\%$ significance level, there is sufficient evidence to reject the car company’s claim that the mean gas mileage for the luxury sedan is at least $25$ miles per gallon.

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QUESTION IMAGE

Question

Explanation:

Step1: Compare test statistic and critical value

Step2: Make a decision about \(H_0\)

Step3: Interpret the result

Answer: