Question

2. A statewide real estate sales agency, Farm Associates, specializes in selling farm property in the state of Nebraska. Its records indicate that the mean selling time of farm property is 90 days. Because of recent drought conditions, the agency believes that the mean selling time is now greater than 90 days. A statewide survey of 100 farms sold recently revealed that the mean selling time was 94 days, with a standard deviation of 22 days. At the .10 significance level, has there been an increase in selling time?

Answer 1

Answer:

Ther has been an increase in the selling time.

Step-by-step explanation:

Step 1. Specify the null hypotesis

In this case, we have to demonstrate that the selling time is now different than before the drought.

$H_{0}: \mu=90\\H_{1}: \mu\neq 90$

Step 2. Choose a significance level

In this problem, is 0.10

Step 3. Compute the mean

In this case, the mean of the sample is 94.

Step 4. Compute the probability value (p) of obtaining a difference between the mean of the sample and the hypothesided value of μ.

$t=\frac{M-\mu}{s/\sqrt{N}} =\frac{94-90}{22/\sqrt{100} }=\frac{4}{2.2} = 1.818$

The degrees of freedom are calculated as (N-1) = (100-1) = 99. Then we can look up in the t-table (http://davidmlane.com/hyperstat/t-table.html) to calculate the probability value of a t of 1.818 with 99 degrees of freedom. The value of this probability is 0.05.

Step 5. Compare the P-value (0.05) with the significance level (0.10). Since the P-value is less than the significance level, the effect is significant.

Since the effect is significant, the null hypotesis is rejected.

It is concluded that the mean of the selling time has changed (increase) from its previous value.