A used car dealer says that the mean price of a three-year-old sports utility vehicle is
$19,000.
You suspect this claim is incorrect and find that a random sample of
25
similar vehicles has a mean price of
$19,675
and a standard deviation of
$1992.
Is there enough evidence to reject the claim at
α=0.01?
Complete parts (a) through (e) below. Assume the population is normally distributed.
Extracted text: A used car dealer says that the mean price of a three-year-old sports utility vehicle is $19,000. You suspect this claim is incorrect and find that a random sample of 25 similar vehicles has a mean price of $19,675 and a standard deviation of $1992. Is there enough evidence to reject the claim at a = 0.01? 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 H, and Ha? OC. Ho: H = $19,000 Ο Α. H : μ > $19,000 H3:us $19,000 Ο Β. Η0: μ= $19,000 Hạ:u> $19,000 Ha: µ< $19,000="" ο="" d="" .="" hρ:="" μ="$19,000" ha:="" u="$19,000" of.="" ho:="" h="$19,000" haiu="$19,000" o="" e.="" ho:="" h2="" $19,000="" h3i="">< $19,000="" (b)="" find="" the="" critical="" value(s)="" and="" identify="" the="" rejection="" region(s).="" what="" is(are)="" the="" critical="" value(s),="" to?="" to="O" (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="" b.=""><><>< o="" c.="">< and="" t=""> O D. t> (c) Find the standardized test statistic t. (Round to two decimal places as needed.) t3D (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 in the rejection region(s) OC. Reject Ho because the test statistic is not in the rejection region(s). O D. Fail to reject H, because the test statistic is not in the rejection region(s). (e) Interpret the decision in the context of the original claim. O A. At the 1% level of significance, there is sufficient evidence to reject the claim that the mean price is not $19,00. O B. At the 1% level of significance, there is not sufficient evidence to reject the claim that the mean price is not $19,000. OC. At the 1% level of significance, there is sufficient evidence to reject the claim that the mean price is $19,000. O D. At the 1% level of significance, there is not sufficient evidence to reject the claim that the mean price is $19,000.