Question

Homes for Sale A real estate agent is interested in the current housing prices in a particular neighborhood in New York. A random sample of 30 homes for sale in the neighborhood was taken and the current listed price of each home was recorded. The data can be found in the JMP file “HomesForSale-NY-S2019.jmp”

(c) Report the degrees of freedom associated with the t-distribution required to construct a confidence interval for the mean for these data.

Distributions Price 3500 3000 2500 2000 1500 1000 500 0 Quantiles 100.0% maximum 99.5% 97.5% 90.0% 75.0% quartile 50.0% median 25.0% quartile 10.0% 2.5% 0.5% 0.0% minimum 3013 3013 3013 1499.8 595.75 302.5 184 136.4 118 118 118 Summary Statistics Mean Std Dev Std Err Mean 576.36667 697.55907 127.35628 Upper 95% Mean 836.8395 Lower 95% Mean 315.89383 30

(d) Based on your answer in (c), what is the value of t ∗ for the 95% confidence interval for the mean price of homes (in thousands of dollars)? (Obtain t ∗ from the t-table (table D), accurate to 3 decimal places.)

(e) What is the margin of error for the above 95% confidence interval? (Round your answer to the nearest 2 decimal places.)

(f) Calculate the 95% confidence interval for the mean price of homes (in thousands of dollars), using your answers from parts (a)-(d). Answer this question by answering the questions below: i. What is the value of the lower bound of the 95% confidence interval?

ii. What is the value of the upper bound of the 95% confidence interval?

Answer 1

(c)

Degree of freedom = n - 1 = 30 - 1 = 29

(d)

Critical value of t for df = 29 and 95% confidence interval is 2.045

(e)

Standard error of mean = 127.35628

Margin of error = t * Standard error of mean = 2.045 * 127.35628 = 260.44

(f)

Sample mean = 576.36667

95% confidence interval is,

(576.36667 - 260.44, 576.36667 + 260.44)

(315.92667,  836.80667)

(i)

lower bound of the 95% confidence interval = 315.92667

ii.

upper bound of the 95% confidence interval = 836.80667