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 30 homes in City A is $127,466. Assume the population standard deviation is $25,877. The mean home sales price for 30 homes in City B is $112,349. Assume the population standard deviation is $27,108. At alpha=0.01, is there enough evidence to reject the agency's claim? Complete parts (a) through (d) below. (a) Identify the claim and state H_0 and_1Ha. What is the claim?

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

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

The calculated value t = 2.1731 < 2.3924 at 0.01 level of significance

The null hypothesis is accepted

Step-by-step explanation:

Step(i):-

Given data The mean home sales price for 30 homes in City A is $127,466

Mean of the first sample(x₁⁻) = $127,466

Standard deviation of the first sample(s₁) =  $25,877

The mean of the second sample(x₂⁻) = $112,349

standard deviation of the second sample(s₂) = $27,108

sample size n₁ = n₂ = 30

Step(ii):-

Null hypothesis : H₀ : The mean home sales price in City A is the same as in City B.

Alternative Hypothesis:H₁: The mean home sales price in City A is the not same as in City B.

The test statistic

where

On calculation ,we get

Test statistic

     t = 2.1731

Degrees of freedom

                            γ = n₁ +n₂ -2

                             γ  = 30+30-2 =58

Conclusion:-

The calculated value t = 2.1731 < 2.3924 at 0.01 level of significance

The null hypothesis is accepted

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

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