Question

Russell is doing some research before buying his first house. he is looking at two different areas of the city, and he wants to know if there is a significant difference between the mean prices of homes in the two areas. for the 35 homes he samples in the first area, the mean home price is $183,100 . public records indicate that home prices in the first area have a population standard deviation of $21,505 . for the 34 homes he samples in the second area, the mean home price is $197,000 . again, public records show that home prices in the second area have a population standard deviation of $25,275 . let population 1 be homes in the first area and population 2 be homes in the second area. construct a 90% confidence interval for the true difference between the mean home prices in the two areas. round the endpoints of the interval to the nearest whole number, if necessary.

Answer 1

To construct a 90% confidence interval for the true difference between two mean values, we use the formula CI = (X1 - X2) ± Z * sqrt((s1^2 / n1) + (s2^2 / n2)). Plugging in the given values, we calculate a confidence interval of approximately -$2,619 to -$25,181.

Step-by-step explanation:

To construct a 90% confidence interval for the true difference between the mean home prices in the two areas, we can use the formula:

CI = (X1 - X2) ± Z * sqrt((s1^2 / n1) + (s2^2 / n2))

Where:

• X1 and X2 are the sample means
• Z is the Z-score corresponding to the desired confidence level (in this case, 90%)
• s1 and s2 are the standard deviations
• n1 and n2 are the sample sizes

Plugging in the given values:

• X1 = $183,100
• X2 = $197,000
• s1 = $21,505
• s2 = $25,275
• n1 = 35
• n2 = 34
• Z = 1.645 (obtained from the standard normal distribution table)

Calculating the confidence interval:

CI = ($183,100 - $197,000) ± 1.645 * sqrt((($21,505)^2 / 35) + (($25,275)^2 / 34))

CI = -$13,900 ± $11,719

Rounding the endpoints to the nearest whole number, the 90% confidence interval for the true difference between the mean home prices in the two areas is approximately -$2,619 to -$25,181.