Question

A real estate association for a specific city puts the average price at which a house was sold in a given year at

$ 259 comma 109$259,109.

Assume that the standard deviation of the house prices is

​$116 comma 088116,088.

Suppose a researcher did a survey of a random selection of

3434

house sale prices in this year and obtained an average house price of

$ 286 comma 489$286,489.

​What's the chance that such a survey would have resulted in an average price this high or​ higher?

Answer 1

The question is asking us to find the p value.

For this we need top understand the number of tails and type of test (t or z)

The Hypothesis:

H0: = 259,109

Ha: 259,109

This is a 2 tailed test.

The Test Statistic: Since the population standard deviation is known and n > 30, we use the z distribution.

The test statistic is given by the equation:

The p Value:    The p value (2 tailed) for Z = 1.38, is; p value = 0.1676

(The definition of the p value is the probability of getting a tests statistic as high as or greater than the one obtained assuming the null hypothesis to be true)