A used car dealer says that the mean price of a three-year-old sports utility vehicle is $24,000. You suspect this claim is incorrect and find that a random sample of 22 similar vehicles has a mean price of $24,623 and a standard deviation of$1964. Is there enough evidence to reject the claim at a = 0.05? Complete parts (a) through (e) below. Assume the population is normally distributed......(a) Write the claim mathematically and identify Ho and Ha.Which of the following correctly states Ho and H,?O A. Ho: µ> $24,000Hai Hs $24,000B. Ho: µ2 $24,000Ha:u< $24,000C. Ho: µ= $24,000Hai H# $24,000Ο D. H0: μ= $24,000Ha: H< $24,000O E. Ho: µ# $24,000Ha: µ= $24,000O F Ho: μ= $24,000Hai H > $24,000%3D(b) Find the critical value(s) and identify the rejection region(s).What is(are) the critical value(s), to?to =0(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.O C. t<and t>O D. t<(c) Find the standardized test statistic t.t =(Round to two decimal places as needed.) (d) Decide whether to reject or fail to reject the null hypothesis.O A. Fail to reject H, because the test statistic is in the rejection region(s).O B. Reject H, because the test statistic is not in the rejection region(s).O C. Fail to reject Ho because the test statistic is not in the rejection region(s).D. Reject Ho because the test statistic is in the rejection region(s).(e) Interpret the decision in the context of the original claim.A. At the 5% level of significance, there is sufficient evidence to reject the claim that the mean price is $24,000.B. At the 5% level of significance, there is not sufficient evidence to reject the claim that the mean price is $24,000.C. At the 5% level of significance, there is sufficient evidence to reject the claim that the mean price is not $24,000.O D. At the 5% level of significance, there is not sufficient evidence to reject the claim that the mean price is not $24,000.

Given data : sample size, n =22 sample mean, x̄ = 24623 sample standard deviation,s= 1964 population mean,μ= 24000 Significance level, α= 0.05solution : a) Hypothesis test : The null and alternative hypothesis is H0: u = 24000 Ha: u ≠ 24000 The hypothesis test is a two tailed testb) critical value : critical value at α =0.05 and df=21 is to=±2.08 Excel formula: =TINV.2T(0.05,21) critical values are -2.08,2.08 Rejection region Reject Ho if t< - 2.08 and t >2.08 c) Test statistic : test statistic for one sample t test is =(24623 - 24000 )/(1964/V22 ) = 1.49 The test statistic is 1.49d) As t <2.08 we failed to reject the null hypothesis Decision is failed reject Ho therefore C) Fail to reject Ho because the test statistic is not in the rejection region(s). e) At the 5% level of significance, there is not sufficient evidence to reject the claim that the mean price is $24,000.