Question

Recently, six single-family homes in San Luis Obispo County in California sold at the following prices (in $1,000s): 696, 660, 900, 605, 826, 669. [You may find it useful to reference the t table.]

a. Construct the 90% confidence interval for the mean sale price in San Luis Obispo County. (Round intermediate calculations to at least 4 decimal places, "sample mean" and "sample standard deviation" to 2 decimal places. Round "t" value to 3 decimal places and final answers to 2 decimal places.)

b. What assumption have you made when constructing this confidence interval?

• Single family homes in San Luis Obispo follow a normal distribution.

• Single family homes in San Luis Obispo need not follow a normal distribution.

Answer 1

A) = (696 + 660 + 900 + 605 + 826 + 669)/6 = 726

S = sqrt(((696 - 726)^2 + (660 - 726)^2 + (900 - 726)^2 + (605 - 726)^2 + (826 - 726)^2 + (669 - 726)^2)/5) = 112.63

At 90% confidence interval the critical value is t^* = 2.015

The 90% confidence interval for population mean is

+/- t^* * s/

= 726 +/- 2.015 * 112.63/

= 726 +/- 92.65

= 633.35, 818.65

B) Single family homes in San Luis Obispo follow a normal distribution.