Question

A used car dealer says that the mean price of a three-year-old sports utility vehicle is $20,000. You suspect this claim is incorrect and find that a random sample of 22 similar vehicles has a mean price of $20,674 and a standard deviation of $1943. 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 H, and H. Which of the following correctly states Ho and H,? O A. Ho: p= $20,000 H <$20,000 OD. Ho: p= $20,000 H+S20,000 O B. Ho u = $20,000 HP> $20,000 O E. Ho:p> $20,000 Hus $20,000 OC. Ho H2 $20,000 Hu<$20,000 0 F. Họ u=520,000 H = $20,000 (b) Find the critical value(s) and identify the rejection region(s). What is(are) the critical value(s), to? (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.) Ов. O At OC. t> OD. < and t>

Answer 1

a)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 20000
Alternative Hypothesis, Ha: μ ≠ 20000

b)

Rejection Region
This is two tailed test, for α = 0.01 and df = 21
Critical value of t are -2.831 and 2.831.
Hence reject H0 if t < -2.831 or t > 2.831

c)

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (20674 - 20000)/(1943/sqrt(22))
t = 1.627

d)

fail to reject null hypothesis.

OPtion D) is answer

e)

OPtion C) is answer