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. a. use a normal sampling distribution because the population is normal, and \\( \sigma \\) is unknown. b. use a t - sampling distribution because \\( n<30 \\). c. use a normal sampling distribution because \\( n>30 \\). d. use a normal sampling distribution because the population is normal, and \\( \sigma \\) is known. e. use a t - sampling distribution because the population is normal, and \\( \sigma \\) is known. f. use a t - sampling distribution because the population is normal, and \\( \sigma \\) is unknown. 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. (round to two decimal places as needed.)

Explanation:

Step1: Determine the sampling distribution

Since the population is normally distributed and the population standard deviation \(\sigma\) is unknown (we are given the sample standard deviation \(s = 2\)), we use the \(t -\)sampling distribution. The formula for the \(t -\)test statistic is \(t=\frac{\bar{x}-\mu}{s/\sqrt{n}}\)

Step2: Identify the values

We are given that \(\bar{x} = 23\) (sample mean), \(\mu = 25\) (claim value), \(s = 2\) (sample standard deviation), and \(n=5\) (sample size)

Step3: Calculate the \(t -\)test statistic

Substitute the values into the formula:

$$
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$$

Answer:

The standardized test statistic is \(-2.24\)