You have been hired by a regional real estate company to determine...

You have been hired by a regional real estate company to determine if the Pacific region's housing prices and housing square footage are significantly different from those of the national market. The regional sales director has three questions that they want to see addressed in the report:

1. Are housing prices in thePacific Region market lower than the national market average?
2. Is the square footage for homes in the Pacific Region region different than the average square footage for homes in the national market?
3. For the Pacific region what is the range of values for the 95% confidence interval of square footage for homes in your market?
4. Define two hypothesis questions and the appropriate type of test for each. Address the following for each hypothesis:
   1. Describe the population parameter for the variable you are analyzing.
   2. Describe your hypothesis in your own words.
   3. Identify the hypothesis test you will use (1-Tail or 2-Tail).
5. Summarize your sample data using appropriate graphical displays and summary statistics and confirm assumptions have not been violated to form this hypothesis test.
6. Summarize your sample data, describing the center, spread, and shape in comparison to the national information (under Supporting Materials, see the National Summary Statistics and Graphs House Listing Price by Region PDF). Note: For shape, think about the distribution: skewed or symmetric.
7. Check the conditions.
   1. Determine if the normal condition has been met.
   2. Determine if there are any other conditions that you should check and whether they have been met. Note: Think about the central limit theorem and sampling methods.

8. Interpret your hypothesis test results using the p value method to reject or not reject the null hypothesis:

1. Relate the p value and significance level.
2. Make the correct decision (reject or fail to reject).
3. Provide a conclusion in the context of your hypothesis.

9. Tail Test: Hypotheses: Define your hypothesis.

1. Define the population parameter.
2. Write null and alternative hypotheses. Note: For means, define a hypothesis that is not equal to the population parameter.
3. State your significance level.

10. Summarize your sample data, describing the center, spread, and shape in comparison to the national information. Note: For shape, think about the distribution: skewed or symmetric.

1. Check the assumptions.
   1. Determine if the normal condition has been met.
   2. Determine if there are any other conditions that should be checked on and whether they have been met. Note: Think about the central limit theorem and sampling methods.

11. Hypothesis Test: Interpret your hypothesis test results using the p value method to reject or not reject the null hypothesis.

 

1. Compare the p value and significance level.
2. Make the correct decision (reject or fail to reject).
3. Provide a conclusion in the context of your hypothesis.

12. Comparison of the test results: For your region, what is the range of values for the 95% confidence interval of square footage for homes? Calculate and report the 95% confidence interval. Show or describe your method of calculation.

13. Summarize your findings: In one paragraph, summarize your findings in clear and concise plain language.

Discuss: Discuss whether you were surprised by the findings. Why or why not?

Data:

National average listing price of homes: $288,407

Sample Mean: $487,985

Sample Standard Deviation: 272936.532

Standard Error: 12206.0928

Null Hypothesis: ​​ u=288,407

Alternative Hypothesis: u<288,407

Level of Significance: 0.05

Test Statistic:-1.26743818

P-Value: 0.1027949

Conclusion: Since the P-Value is more than the level of significance we will fail to reject the null hypothesis 

Interpretation: There is no significant evidence that the avg listing price in the Pacific region is lower than the national avg listing price. 

National average square footage of homes:1,944Ft

Sample Mean:1,897

Sample Standard Deviation: 236.6588558

Standard Error:10.5837059

Null Hypothesis: u=1,944

Alternative Hypothesis: u≠1,944

Level of Significance: 0.05

Test Statistic: 179.265833

P-Value: 0

Conclusion:Since the p-value is less than the level of signifance, we will reject the null hypothesis

Interpretation:There is evidence that the avg sq ft in the Pacific region is not equal to the national avg sq ft

95% Confidence Interval

Alpha:0.05

Margin Of Error:20.794118

Lower Bound: 1,877

Upper Bound: 1,918

(1,877, 1,918)