Question

A family is relocating from St. Louis, Missouri, to California. Due to an increasing inventory of houses in St. Louis, it is taking longer than before to sell a house. The wife is concerned and wants to know when it is optimal to put their house on the market. Her realtor friend informs them that the last 28 houses that sold in their neighborhood took an average time of 220 days to sell. The realtor also tells them that based on her prior experience, the population standard deviation is 40 days. [You may find it useful to reference the z table.]

b. Construct the 95% confidence interval for the mean sale time for all homes in the neighborhood. (Round intermediate calculations to at least 4 decimal places. Round "z" value to 3 decimal places and final answers to 2 decimal places.)

	Confidence interval to

Answer 1

Solution :

Given that,

= 220

= 40

n = 28

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

Margin of error = E = Z_/2* ( /n)

= 1.96 * (40 / 28)

= 14.82

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

- E < < + E

220 -14.82 < < 220 + 14.82

205.18 < < 234.82

Confidence interval : 205.18 to 234.82