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.

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