The housing market in my area has seen a 12% trend downward in the average price. Further, the time to closing appears to have taken more time as compared to 3 years ago.

Question

The housing market in my area has seen a 12% trend downward in the average price. Further, the time to closing appears to have taken more time as compared to 3 years ago.

Here are the values for the average time to close for the houses in the area.
Mean = 22.3 weeks Std deviation = 5.5
Sampling 30 houses, and using a 95% confidence, would you expect the time to close to be 24 weeks?
Why or why not?

Answer 1

To answer this question, we can use a hypothesis test to compare the sample mean time to close (22.3 weeks) with the given value of 24 weeks. We will assume that the population standard deviation is the same as the sample standard deviation (5.5 weeks).

Here are the steps to conduct this hypothesis test:

Step 1: State the hypotheses:
- Null hypothesis (H0): The population mean time to close is equal to 24 weeks.
- Alternative hypothesis (H1): The population mean time to close is not equal to 24 weeks.

Step 2: Set the significance level (α):
The given question does not specify the significance level (α), so let's assume α = 0.05 (which corresponds to a 95% confidence level).

Step 3: Collect data and calculate the test statistic:
We are given the sample mean (22.3 weeks), the population standard deviation (5.5 weeks), and the sample size (30 houses). We will use these values to calculate the test statistic (Z-score) using the formula:
Z = (sample mean - population mean) / (population standard deviation / √sample size)

Z = (22.3 - 24) / (5.5 / √30)

Step 4: Calculate the p-value:
Using the test statistic (Z-score), we can calculate the p-value associated with the observed sample mean. The p-value represents the probability of obtaining a sample mean as extreme as the one observed, assuming the null hypothesis is true.

Step 5: Make a decision:
If the p-value is less than the significance level (α), we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

So, based on the given information and the calculated p-value, we can determine whether to expect the time to close to be 24 weeks.

Note: Since we do not have the actual values for the sample mean, population mean, standard deviation, and sample size in this scenario, I cannot provide the specific result. However, you can follow the steps outlined above and use the actual values to obtain the statistical conclusion.