A used car dealer says that the mean price of a three-year-old sports utility vehicle is $21,000. You suspect this claim is incorrect and find that a random sample of 25 similar vehicles has a mean price of $21,571 and a standard deviation of $1991. Is there enough evidence to reject the claim at $\alpha = 0.10$? Complete parts (a) through (e) below. Assume the population is normally distributed.
(a) Write the claim mathematically and identify $H_0$ and $H_a$.
Which of the following correctly states $H_0$ and $H_a$?
A. $H_0: \mu = \$21,000$
$H_a: \mu < \$21,000$
B. $H_0: \mu = \$21,000$
$H_a: \mu > \$21,000$
C. $H_0: \mu = \$21,000$
$H_a: \mu \ne \$21,000$
D. $H_0: \mu = \$21,000$
$H_a: \mu = \$21,000$
E. $H_0: \mu > \$21,000$
$H_a: \mu \le \$21,000$
F. $H_0: \mu = \$21,000$
$H_a: \mu < \$21,000$
(b) Find the critical value(s) and identify the rejection region(s).
What is(are) the critical value(s), $t_0$?
$t_0 = \boxed{}$
(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. $t < \boxed{}$
B. $\boxed{} < t < \boxed{}$
C. $t > \boxed{}$
D. $t < \boxed{} \text{ and } t > \boxed{}$
(c) Find the standardized test statistic t
$t = \boxed{}$ (Round to two decimal places as needed.)
(d) Decide whether to reject or fail to reject the null hypothesis.
A. Fail to reject $H_0$ because the test statistic is in the rejection region(s).
B. Fail to reject $H_0$ because the test statistic is not in the rejection region(s).
C. Reject $H_0$ because the test statistic is in the rejection region(s).
