Question

1. The table below gives selling prices for 24 houses in the fictional SE Portland neighborhood of Westsellstock in July 2016. (Numbers are in thousands of dollars.) 315 310 314 337 288 292 277 267 336 361 169 339 295 318 271 241 288 241 345 321 340 306 228 314 •

Find the mean and standard deviation of the prices of these 24 houses.

What conditions and assumptions do you need to check to create a confidence interval for the mean price of houses in Westsellstock?

To create a 95% confidence interval, we need to know the value of t* for a sample this size. What is that value? (Looking it up in a table is the easiest.)

Create the 95% confidence interval. (It’s okay if the conditions aren’t met.)

Interpret the interval with a sentence. (Be sure your sentence includes the context of this situation, so it should be about house prices.)

Answer 1

= (315 + 310 + 314 + 337 + 288 + 292 + 277 + 267 + 336 + 361 + 169 + 339 + 295 + 318 + 271 + 241 + 288 + 241 + 345 + 321 + 340 + 306 + 228 + 314)/24 = 296.375

S = sqrt(((315 - 296.375)^2 + (310 - 296.375)^2 + (314 - 296.375)^2 + (337 - 296.375)^2 + (288 - 296.375)^2 + (292 - 296.375)^2 + (277 - 296.375)^2 + (267 - 296.375)^2 + (336 - 296.375)^2 + (361 - 296.375)^2 + (169 - 296.375)^2 + (339 - 296.375)^2 + (295 - 296.375)^2 + (318 - 296.375)^2 + (271 - 296.375)^2 + (241 - 296.375)^2 + (288 - 296.375)^2 + (241 - 345)^2 + (321 - 296.375)^2 + (340 - 296.375)^2 + (306 - 296.375)^2 + (228 - 296.375)^2 + (314 - 296.375)^2)/23) = 44.172

Since the sample size is not large, so We should assume that the population is normally distributed.

At 95% confidence interval the critical value is t^* = 2.069

The 95% confidence interval is

+/- t^* * S/

= 296.375 +/- 2.069 * 44.172/

= 296.375 +/- 18.655

= 277.72 , 315.03

We are 95% confident that the true population mean lies in the above confidence interval.