Question

A used car dealer says that the mean price of a​ three-year-old sports utility vehicle is

​$23,000.

You suspect this claim is incorrect and find that a random sample of

21

similar vehicles has a mean price of

​$23,530

and a standard deviation of

​$1952.

Is there enough evidence to reject the claim at

α=0.10​?

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>​$23,000

Ha​:

μ≤​$23,000

B.

H0​:

μ=​$23,000

Ha​:

μ≠​$23,000

C.

H0​:

μ=​$23,000

Ha​:

μ>​$23,000

D.

H0​:

μ≠​$23,000

Ha​:

μ=​$23,000

E.

H0​:

μ≥​$23,000

Ha​:

μ<​$23,000

F.

H0​:

μ=​$23,000

Ha​:

μ<​$23,000

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

What​ is(are) the critical​ value(s),

t0​?

t0=nothing

​(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.

nothing<t<nothing

B.

t<nothing

C.

t<nothing

and

t>nothing

D.

t>nothing

​(c) Find the standardized test statistic t.

t=nothing

​(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.

Reject

H0

because the test statistic

is

in the rejection​ region(s).

C.

Fail to reject

H0

because the test statistic

is not

in the rejection​ region(s).

D.

Reject

H0

because the test statistic

is not

in the rejection​ region(s).

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

A.At the

10​%

level of​ significance, there

is

sufficient evidence to reject the claim that the mean price is $23,000.

B.At the

10​%

level of​ significance, there

is not

sufficient evidence to reject the claim that the mean price is $23,000.

C.At the

10​%

level of​ significance, there

is not

sufficient evidence to reject the claim that the mean price is not $23,000.

D.At the

10​%

level of​ significance, there

is

sufficient evidence to reject the claim that the mean price is not

Answer 1

a)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 23000
Alternative Hypothesis, Ha: μ ≠ 23000

b)

Rejection Region
This is two tailed test, for α = 0.1 and df = 20
Critical value of t are (-1.725 , 1.725).
Hence reject H0 if t < -1.725 or t > 1.725

c)

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (23530 - 23000)/(1952/sqrt(21))
t = 1.24

d)

fail to reject null hypothesis.

OPtion C) is answer

e)

OPtion B) is answer