Question

An important factor in selling a residential property is the number of people who look through the home. A sample of 14 homes recently sold in the Buffalo, New York, area revealed the mean number looking through each home was 23 and the standard deviation of the sample was 5 people. Develop a 95% confidence interval for the population mean. (Use t Distribution Table.) (Round your answers to 2 decimal places.)

Answer 1

Solution :

Given that,

= 23

s =5

n =14

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

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

  / 2= 0.05 / 2 = 0.025

t /2,df = t0.025,13 = 2.160 ( using student t table)

Margin of error = E = t/2,df * (s /n)

= 2.160 * (5 / 14)

= 2.87

The 95% confidence interval estimate of the population mean is,

- E < < + E

23 - 2.87 < < 23 + 2.87

(20.13 , 25.87)