Question

a car company says 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 6 cars has a mean gas mileage of 21 mpg and a standard deviation of 3 mpg. at \\( \alpha = 0.10 \\), 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. c. use a t - sampling distribution because the population is normal, and \\( \sigma \\) is unknown. d. use a normal sampling distribution because the population is normal, and \\( \sigma \\) is unknown. e. use a t - sampling distribution because the population is normal, and \\( \sigma \\) is known. f. use a normal sampling distribution because the population is normal, and \\( \sigma \\) is known. state the appropriate hypotheses to test. a. \\( h_0: \mu \geq 23 \\) \\( h_a: \mu < 23 \\) b. \\( h_0: \mu = 23 \\) \\( h_a: \mu \
eq 23 \\) c. \\( h_0: \mu \leq 23 \\) \\( h_a: \mu > 23 \\) d. \\( h_0: \mu \
eq 23 \\) \\( h_a: \mu = 23 \\) what is the value of the standardized test statistic? the standardized test statistic is - 1.63. (round to two decimal places as needed.) what is the critical value? the critical value is \\( \square \\). (round to three decimal places as needed.)

Explanation:

Step1: Determine the degrees of freedom

The degrees of freedom \(df=n - 1\), where \(n = 6\). So \(df=6-1 = 5\).

Step2: Find the critical value for a left - tailed test

Since \(\alpha=0.10\) and it is a left - tailed test (because \(H_{a}:\mu<23\)), we look up the value in the t - distribution table.
For \(df = 5\) and \(\alpha = 0.10\) in the left - tailed test, the critical value \(t_{0}\) is such that \(P(T<t_{0})=\alpha\).
From the t - distribution table, \(t_{0}=- 1.476\)

Answer:

The critical value is \(-1.476\)