A credit card company claims that the mean credit card debt for individuals is greater than

$ 4 comma 700.$4,700.

You want to test this claim. You find that a random sample of

3131

cardholders has a mean credit card balance of

$ 4 comma 873$4,873

and a standard deviation of

$ 650$650.

At

alpha equals 0.01=0.01,

can you support the claim? Complete parts (a) through (e) below. Assume the population is normally distributed.

(a) Write the claim mathematically and identify

Upper H 0H0

and

Upper H Subscript aHa.

Which of the following correctly states

Upper H 0H0

and

Upper H Subscript aHa?

A.

Upper H 0H0:

mugreater than>$4 comma 7004,700

Upper H Subscript aHa:

muless than or equals$4 comma 7004,700

B.

Upper H 0H0:

muequals=$4 comma 7004,700

Upper H Subscript aHa:

mugreater than>$4 comma 7004,700

C.

Upper H 0H0:

muless than or equals$4 comma 7004,700

Upper H Subscript aHa:

mugreater than>$4 comma 7004,700

D.

Upper H 0H0:

muequals=$4 comma 7004,700

Upper H Subscript aHa:

munot equals$4 comma 7004,700

E.

Upper H 0H0:

mugreater than or equals$4 comma 7004,700

Upper H Subscript aHa:

muless than<$4 comma 7004,700

F.

Upper H 0H0:

mugreater than>$4 comma 7004,700

Upper H Subscript aHa:

muless than or equals$4 comma 7004,700

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

What is(are) the critical value(s),

t 0t0?

t 0t0equals=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.

tless than

and

tgreater than>nothing

B.

tgreater than>nothing

C.

nothing less than

D.

tless than

(c) Find the standardized test statistic t.

tequals=nothing

(Round to two decimal places as needed.)

(d) Decide whether to reject or fail to reject the null hypothesis.

A.

RejectReject

Upper H 0H0

because the test statistic

isis

in the rejection region.

B.

Fail to rejectFailtoreject

Upper H 0H0

because the test statistic

isis

in the rejection region.

C.

Fail to rejectFailtoreject

Upper H 0H0

because the test statistic

is notisnot

in the rejection region.

D.

RejectReject

Upper H 0H0

because the test statistic

is notisnot

in the rejection region.

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

At the

11%

level of significance, there

is notisnot

sufficient evidence to support the claim that the mean credit card debt is less than

$4 comma 7004,700.

B.

At the

11%

level of significance, there

isis

sufficient evidence to support the claim that the mean credit card debt is greater than

$4 comma 7004,700.

C.

At the

11%

level of significance, there

is notisnot

sufficient evidence to support the claim that the mean credit card debt is greater than

$4 comma 7004,700.

D.

At the

11%

level of significance, there

isis

sufficient evidence to support the claim that the mean credit card debt is less than

$4 comma 7004,700.