Question

An important factor in selling a residential property is the number of people who look through the home. A sample of 27 homes recently sold in the Halifax, Nova Scotia, area revealed the mean number looking through each home was 49 and the standard deviation of the sample was 10 people. Develop a 95% confidence interval for the population mean. (Round the final answers to 2 decimal places.)

Confidence interval for the population mean is between and .

Answer 1

Solution :

Given that,

= 49

s =10

n = 27

Degrees of freedom = df = n - 1 =27 - 1 = 26

a ) At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

  / 2= 0.05 / 2 = 0.025

t /2,df = t0.025,26 = 2.056 ( using student t table)

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

= 2.056* (10 / 27)

= 3.96

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

- E < < + E

49 - 3.96< <49 + 3.96

45.04< < 52.96

( 45.04, 52.96 )