Question

Suppose that a random sample of fourteen recently sold houses in a certain city has a mean sales price of $275,000, with a standard deviation of $11,000. Under the assumption that house prices are normally distributed, find a 90% confidence interval for the mean sales price of all houses in this community. Then complete the table below. Carry your intermediate computations to at least three decimal places. Round your answers to the nearest whole number (If necessary, consult a list of formulas.) What is the lower limit of the confidence interval? What is the upper limit of the confidence interval? x 5 ?

Answer 1

solution:-

given that

mean = 275000 , standard deviation = 11000

sample n = 14

degree of freedom df = n - 1 - 14 - 1 = 13

the value of 90% confidence with df from t table is t = 1.771

confidence interval formula

=> mean +/- t * standard deviation/sqrt(n)

=> 275000 +/- 1.771 * 11000/sqrt(14)

=> (269793 , 280207)

lower limit = 269793

upper limit = 280207