Question

a used car dealer says that the mean price of a three - year - old sports utility vehicle is $22,000. you suspect this claim is incorrect and find that a random sample of 24 similar vehicles has a mean price of $22,873 and a standard deviation of $1972. is there enough evidence to reject the claim at \\( \alpha=0.05 \\)? complete parts (a) through (e) below. assume the population is normally distributed. which of the following correctly states \\( h_0 \\) and \\( h_a \\)? a. \\( h_0: \mu=$22,000 \\) \\( h_a: \mu>$22,000 \\) b. \\( h_0: \mu\
eq$22,000 \\) \\( h_a: \mu=$22,000 \\) c. \\( h_0: \mu=$22,000 \\) \\( h_a: \mu\
eq$22,000 \\) d. \\( h_0: \mu=$22,000 \\) \\( h_a: \mu<$22,000 \\) e. \\( h_0: \mu>$22,000 \\) \\( h_a: \mu\leq$22,000 \\) f. \\( h_0: \mu\geq$22,000 \\) \\( h_a: \mu<$22,000 \\) (b) find the critical value(s) and identify the rejection region(s). what is(are) the critical value(s), \\( t_0 \\)? \\( t_0=-2.069,2.069 \\) (use a comma to separate answers as needed. round to three decimal places as needed.) determine the rejection region(s). select the correct choice below and fill in the answer box(es) within your choice. (round to three decimal places as needed.) a. \\( t< \\)? b. \\( t< \\) and \\( t> \\) c. \\( \\)

Explanation:

Step1: Determine the type of hypothesis test

Since the alternative hypothesis \(H_{a}:\mu
eq22000\), this is a two - tailed test.

Step2: Find the degrees of freedom

The degrees of freedom \(df=n - 1\), where \(n = 24\). So \(df=24-1=23\).

Step3: Locate the critical values

For a two - tailed test with \(\alpha = 0.05\) and \(df = 23\), using the t - distribution table, the critical values \(t_{0}\) are \(t=- 2.069\) and \(t = 2.069\).

Step4: Identify the rejection regions

For a two - tailed t - test, the rejection regions are \(t<-2.069\) and \(t>2.069\).

Answer:

The critical values are \(-2.069\) and \(2.069\). The rejection regions are \(t < - 2.069\) and \(t>2.069\), so the correct choice for the rejection region is \(B\) where \(t < - 2.069\) and \(t>2.069\).