Question

Beatrice has received two job offers, one in city A and one in city B. She would like to estimate the difference in average home prices for the two cities. From a random sample of 40 listings in city A, the average home price is $189500. For a random sample of 40 listings in city B, the average home price is $185000. She finds the margin of error for 95% confidence interval for the difference in average home price between the two cities (A-B) to be $3400.(a) Which of the following conclusions is correct?O Beatrice can be 95% confident that there is not a significant difference in the average home price between these two cities.
O Beatrice can be 95% confident that the average home price is between $1100 and $7900 more in city A than in city B.
O Beatrice can be 95% confident that the average home price is $4500 more in city A than in city B.
O Beatrice can be 95% confident that the average home price is between $1100 and $7900 less in city A than in city B.
O Beatrice can be 95% confident that the average home price is $4500 less in city A than in city B.

Answer 1

Answer:

Step-by-step explanation:

The confidence interval gives a range of values that could contain the population mean.

Confidence interval is written as

Sample mean ± margin of error

Confidence interval does not express probability.

Given that the sample mean home price for city A is $189500 and the sample mean home price for city B is $185000, the difference in the sample mean home prices for both cities is

189500 - 185000 = $4500

Since the margin of error for 95% confidence interval for the difference in average home price between the two cities (A-B) to be $3400, then

The upper limit of the confidence interval is

4500 + 3400 = $7900

The lower limit of the confidence interval is

4500 - 3400 = $1100

Therefore, the correct conclusion is

Beatrice can be 95% confident that the average home price is between $1100 and $7900 more in city A than in city B.