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.
(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< - 2.069 \\) and \\( t>2.069 \\)
c. \\( d. \\( t> \\)
(c) find the standardized test statistic t.
\\( t = 2.17 \\) (round to two decimal plact as needed.)
(d) decide whether to reject or fail to reject the null hypothesis.
a. reject \\( h _ { 0 } \\) because the test statistic is in the rejection region(s).
b. fail to reject \\( h _ { 0 } \\) because the test statistic is in the rejection region(s).
c. fail to reject \\( h _ { 0 } \\) because the test statistic is not in the rejection region(s).
d. reject \\( h _ { 0 } \\) because the test statistic is not in the rejection region(s).

Explanation:

Step1: Identify the rejection region

The rejection region is \(t < - 2.069\) and \(t>2.069\) (given in part (b) as option B).

Step2: Compare the test - statistic with the rejection region

The standardized test statistic \(t = 2.17\).
Since \(2.17>2.069\), the test statistic \(t = 2.17\) lies in the rejection region.

Answer:

A. Reject \(H_0\) because the test statistic is in the rejection region(s).