Question

Mr. Zillow wants to research the prices in a Subdivision near Disney World called World of Homes. The prices of 14 homes in this subdivision are listed below. As a conclusion for his research, with a 90% confidence level, he prepares a report indicating the confidence interval for the mean prices of "World of Homes".

World of Homes Prices:

$225,000 $320,000 $219,000 $199,000 $275,000 $300,000 $215,000
$210,000 $307,000 $285,000 $317,000 $195,000 $205,000 $286,000


In his report for the mean prices of "World of Homes", he first presents the value of margin of error which is equal to ___ along with the value of degrees of freedom which is equal to ___.

Moreover, Mr. Zillow's report also indicates the mean prices of "World of Homes" with a lower limit of ___ and an upper limit of ___ with a confidence level of 90%.

Answer 1

Looking for four values or answers

(A) 5.05

(B) 13

(C) $254,140.33

(D) $254,145.38

Explanation:

(A) The value of the margin of error.

Using a 90% confidence level or 0.10 alpha level,

1 - alpha = 1 - 0.10 = 0.90

The degrees of freedom = n - 1 = 14 - 1 = 13

Using the t table, 0.90 under 13 is 1.350

Sample size divided by √n is equal to

14/√14 = 3.742

1.35 × 3.742 = 5.05

(B) 13 degrees of freedom

(C) To find the lower and upper limits, you find the mean value first and then subtract / add to half of the margin of error which is 5.05÷2 = 2.525

Adding the 14 values together, you have $3,558,000

Dividing by 14 to get the mean;

Mean = $254,142.8571

Lower Limit: $254,140.33

Upper Limit: $254,145.38