Can you confirm that my answers are correct?

A real estate agency says that the mean home sales price in City A is the same as in City B. The mean home sales price for 25

25 homes in City A is $127 comma 421

127,421. Assume the population standard deviation is $25 comma 880

25,880. The mean home sales price for 25

25 homes in City B is $112 comma 284

112,284. Assume the population standard deviation is $27 comma 109

27,109. At alpha

equals

=0.01

0.01, is there enough evidence to reject theagency's claim? Complete parts(a) through(d) below.

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a) Identify the claim and state Upper H 0

H0 and Upper H Subscript a

Ha.

What is theclaim? (D)

A.

The mean home sales price in City A is not the same as in City B.

B.

The mean home sales price in City A is less than in City B.

C.

The mean home sales price in City A is greater than as in City B.

D.

The mean home sales price in City A is the same as in City B.

Let City A be sample 1 and let City B be sample 2. Identify H0 and Ha.

H0: mu 1 1= mu 2 2

(b) Find the criticalvalue(s) and identify the rejection region. Select the correct choice below and fill in the answer box within your choice.

(Round to three decimal places asneeded.) (B)

A.

The critical value is z 0 z0equals=nothing

B.

The critical values are z 0

z0=plus or minus2.576

What is the rejectionregion? Select the correct choice below and fill in the answerbox(es) within your choice.

(Round to three decimal places asneeded.) (A)

A.

z<2.576 or z >2.576

B.

z<

nothing

C.

z>

nothing

(c) Find the standardized test statistic z.

z=1.91

(Round to two decimal places asneeded.)

(d) Decide whether to reject or fail to reject the null hypothesis and interpret the decision in the context of the original claim.

Fail to reject H0. There is not enough evidence at the 1% level of significance to reject theagency's claim that the mean home sales price in City A is the same as the same as in City B.