Question

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.

Answer 1

The test value is z = -1.31.

Explanation:

The Eagle Ridge Contractors Association claims the average price of a home in their subdivision is $125,150.

This means that the null hypothesis is that the mean is this value, that is:

`H_0: \mu = 125150`

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.

This means that at the alternate hypotehsis we test that the mean is lower than that value, that is:

`H_a: \mu < 125150`

The test statistic is:

`z = (X - \mu)/((\sigma)/(√(n)))`

In which X is the sample mean,
`\mu` is the value tested at the null hypothesis,
`\sigma` is the standard deviation and n is the size of the sample.

125150 is tested at the null hypothesis:

This means that
`\mu = 125150`

Standard deviation of $7,350.

This means that
`\sigma = 7350`

A sample of 36 homes for sale in this subdivision had an average selling price of $123,550.

This means that
`n = 36, X = 123550`

Compute the test value.

`z = (X - \mu)/((\sigma)/(√(n)))`

`z = (123550 - 125150)/((7350)/(√(36)))`

`z = -1.31`

The test value is z = -1.31.