Question

suppose a random sample of 12 houses on the market have an average asking price of $165,000 with a standard deviation of $28,000. Find a 95% confidence interval for the true mean asking price for houses on the market.

Please show all steps to solving.

Answer 1

Solution :

Degrees of freedom = df = n - 1 = 11

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t _/2,df = t_0.025,11 = 2.201

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

= 2.201 * (28000 / 12)

= 17790.47

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

- E < < + E

165000 - 17790.47 < < 165000 + 17790.47

147209.53 < < 182790.47

($147210 , $182791,)