Question

a car company states that the mean gas mileage for its luxury sedan is at least 23 miles per gallon (mpg). you believe the claim is incorrect and find that a random sample of 7 cars has a mean gas mileage of 20 mpg and a standard deviation of 4 mpg. at a = 0.025, 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. which sampling distribution should be used and why? a. use a t-sampling distribution because the population is normal, and σ is known. b. use a normal sampling distribution because the population is normal, and σ is known. c. use a t-sampling distribution because n < 30 d. use a normal sampling distribution because n > 30. e. use a normal sampling distribution because the population is normal, and σ is unknown f. use a t-sampling distribution because the population is normal, and σ is unknown. state the appropriate hypotheses to test. a. h₀: μ ≥ 23 hₐ: μ < 23 b. h₀: μ ≤ 23 hₐ: μ > 23 c. h₀: μ = 23 hₐ: μ ≠ 23 d. h₀: μ ≠ 23 hₐ: μ = 23

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 $s = 4$), we use a t - sampling distribution.

Step2: State the hypotheses

The company claims that the mean gas mileage $\mu\geq23$ (the null hypothesis $H_0$). We believe the claim is incorrect (so we test against $\mu < 23$). The null hypothesis $H_0:\mu\geq23$ and the alternative hypothesis $H_a:\mu < 23$.

Answer:

For the sampling distribution: Use a t - sampling distribution because the population is normal, and $\sigma$ is unknown.
For the hypotheses: A. $H_0:\mu\geq23$, $H_a:\mu < 23$