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.Is there evidence that the costs of homes for sale in this subdivision are
actually lower than claimed?
-At 0.05, what is the test value?
A)-1.31
B)1.31
C)-1.52
D)1.52

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.Is there evidence that the costs of homes for sale in this subdivision are
actually lower than claimed?
-At  0.05, what is the test value?
A)-1.31 
B)1.31 
C)-1.52 
D)1.52

Quizplus · Accepted Answer

We need to perform a one-sample t-test to determine if there is evidence that the costs of homes for sale in this subdivision are actually lower than claimed. The null hypothesis is that the true population mean selling price is equal to $125,150, and the alternative hypothesis is that the true population mean selling price is less than $125,150.

We can calculate the test statistic using the formula:

t = (sample mean - hypothesized population mean) / (standard deviation / sqrt(sample size))

Plugging in the values, we get:

t = (123,550 - 125,150) / (7,350 / sqrt(36)) = -1.31

At alpha = 0.05 and 35 degrees of freedom (n-1), the critical t-value is -1.69. Since our calculated t-value (-1.31) is greater than the critical t-value (-1.69) and falls within the non-rejection region, we fail to reject the null hypothesis.

Therefore, we do not have evidence to suggest that the costs of homes for sale in this subdivision are actually lower than claimed. The null hypothesis is that the average selling price of homes in the subdivision is equal to or higher than the claimed value, while the alternative hypothesis is that it is lower than the claimed value.
We can use a one-sample t-test with the formula 
t=(x̄-μ)/(s/√n)
where x̄ is the sample mean, μ is the claimed population mean, s is the sample standard deviation, and n is the sample size.
Substituting the given values, we get
t = (123550-125150)/(7350/√36)
= -1.31
Looking at the t-distribution table with 35 degrees of freedom (df=n-1), we find the critical t-value at α=0.05 to be ±2.03. Since our test value of -1.31 falls within the acceptance region (between -2.03 and +2.03), we fail to reject the null hypothesis. There is not enough evidence to claim that the costs of homes for sale in this subdivision are actually lower than claimed at the 5% significance level.

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