The Eagle Ridge Contractors Association claims the average price of a home in their subdivision is $125,150 with a standard deviation of $7,350. A sample of 36 homes for
Sale in this subdivision had an average selling price of $123,550. The Eagle Ridge Home
Owners Association is interested in knowing if the costs of homes for sale in this
Subdivision are actually lower than claimed? Compute the test value.
A) 1.31
B) 1.52
C) -1.31
D) -1.52

Question

Quizplus · Accepted Answer

The test value is calculated using the formula for a z-test: $z = \frac{\bar{x} - \mu}{(\sigma/\sqrt{n})}$, where $\bar{x}$ is the sample mean, $\mu$ is the population mean, $\sigma$ is the population standard deviation, and $n$ is the sample size. Plugging in the given values: $z = \frac{123,550 - 125,150}{(7,350/\sqrt{36})} = \frac{-1,600}{1,225} = -1.31$. This indicates the sample mean is 1.31 standard deviations below the claimed population mean.

The Eagle Ridge Contractors Association Claims the Average Price of a Home