Question

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 21 similar vehicles has a mean price of ​$21,857 and a standard deviation of ​$1976. Is there enough evidence to reject the claim at alphaα=0.05​?

Complete parts​ (a) through​(e) below. Assume the population is normally distributed.​(a) Write the claim mathematically and identify H0 and Ha.

Which of the following correctly states H0 and Ha​?

A.

H0​: μ ≥​ $21,000

Ha​: μ <​ $21,000

B.

H0​: μ ≠ ​$21,000

Ha​: μ = ​$21,000

C.

H0​: μ =​ $21,000

Ha​: μ > ​$21,000

D.

H0​: μ =​ $21,000

Ha​: μ ≠ ​$21,000

E.

H0​: μ > ​$21,000

Ha​: μ ≤ ​$21,000

F.

H0​: μ =​ $21,000

Ha​: μ < ​$21,000

​(b) Find the critical​ value(s) and identify the rejection​ region(s).

What​ is(are) the critical​ value(s) t0​?

t0 = ?

​(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 < ____

C.

t < _____ and t > _____

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.

A.

Fail to reject H0 because the test statistic is in the rejection​ region(s).

B.

Fail to reject H0 because the test statistic is not in the rejection​ region(s).

C.

Reject H0 because the test statistic is not in the rejection​ region(s).

D.

Reject H0 because the test statistic is in the rejection​ region(s).

​(e) Interpret the decision in the context of the original claim.

A.At the

55​% level of​ significance, there is sufficient evidence to reject the claim that the mean price is $21,000.

B. At the 55​% level of​ significance, there is not sufficient evidence to reject the claim that the mean price is $21,000.

C. At the 55​% level of​ significance, there is sufficient evidence to reject the claim that the mean price is not $21,000.

D. At the 55​% level of​ significance, there is not sufficient evidence to reject the claim that the mean price is not $21,000.

Answer 1

(A) Claim is that mean price of a​ three-year-old sports utility vehicle is ​$21,00

so, we have to check whether the mean is equal to $21,000 or not

it is a two sided test

option D for hypothesis is correct

(B)sample size n = 21

degree of freedom = n-1= 21-1 = 20

t critical = T.INV.2T(alpha,df)

= T.INV.2T(0.05,20)

= -2.086 and 2.086

option C, -2.086<t or t> 2.086

(C) Using TI 84 calculator, select TTest

enter the data set

press enter, we get

t sttaistic= 1.99

(D) t statistic is neither less than -2.086 nor greater than 2.086

Fail to reject H0 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 $21,000.

this is because the result is insignificant and failed to reject the null hypothesis.