Question

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 20 homes in City A is ​$127 comma 462. Assume the population standard deviation is ​$25 comma 879. The mean home sales price for 20 homes in City B is ​$112 comma 289. Assume the population standard deviation is ​$27 comma 112. At alphaequals0.01​, is there enough evidence to reject the​ agency's claim? Complete parts​ (a) through​ (d) below. ​(a) Identify the claim and state Upper H 0 and Upper H Subscript a. What is the​ claim? A. The mean home sales price in City A is 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 not the same as in City B. Let City A be sample 1 and let City B be sample 2. Identify Upper H 0 and Upper H Subscript a. Upper H 0​: mu 1 ▼ not equals less than or equals greater than or equals equals mu 2 Upper H Subscript a​: mu 1 ▼ not equals greater than or equals less than less than or equals equals greater than mu 2 ​(b) Find the critical​ value(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 as​ needed.) A. The critical value is z 0equals nothing. B. The critical values are z 0equalsplus or minus nothing. What is the rejection​ region? Select the correct choice below and fill in the answer​ box(es) within your choice. ​(Round to three decimal places as​ needed.) A. zgreater than nothing B. zless than nothing or zgreater than zgreater than nothing C. zless than nothing ​(c) Find the standardized test statistic z. zequals nothing ​(Round to two decimal places as​ needed.) ​(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 Reject Upper H 0. There ▼ is not is enough evidence at the 1​% level of significance to ▼ reject support the​ agency's claim that the mean home sales price in City A is ▼ less than not greater than the same as not less than in City B. Click to select your answer(s).

Answer 1

Given : For city A ; , ,

For city b: , ,

Significance level=

(a) Hypothesis : Vs  

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

(b) The critical value is given by ,

; From the standard normal probability table

Rejection region :

(c) The value of the standardized test statistic is ,

(d) Decision : Here , the value of the test statistic does not lies in the rejection region.

Therefore , fail to reject the null hypothesis.

Interpretation :

Fail to reject Ho. There is enough evidence at the 1​% level of significance to support the​ agency's claim that the mean home sales price in City A is same as in City B.