Competency
In this project, you will demonstrate your mastery of the following competency:
Apply sta!s!cal techniques to address research problems
Perform hypothesis tes!ng to address an authen!c problem
Overview
In this project, you will apply inference methods for means to test your hypotheses about the housing sales market for a region of the United
States. You will use appropriate sampling and sta!s!cal methods.
Scenario
You have been hired by your regional real estate company to determine if your region’s housing prices and housing square footage are significantly
different from those of the na!onal market. The regional sales director has three ques!ons that they want to see addressed in the report:
1. Are housing prices in your regional market higher than the na!onal market average?
2. Is the square footage for homes in your region different than the average square footage for homes in the na!onal market?
3. For your region, what is the range of values for the 95% confidence interval of square footage for homes in your market?
You are given a real estate data set that has houses listed for every county in the United States. In addi!on, you have been given na!onal sta!s!cs
and graphs that show the na!onal averages for housing prices and square footage. Your job is to analyze the data, complete the sta!s!cal
analyses, and provide a report to the regional sales director. You will do so by comple!ng the Project Two Template located in the What to Submit
area below.
Direc!ons
Introduc!on
1. Purpose: What was the purpose of your analysis, and what is your approach?
a. Define a random sample and two hypotheses (means) to analyze.
2. Sample: Define your sample. Take a random sample of 100 observa!ons for your region.
a. Describe what is included in your sample (i.e., states, region, years or months).
3. Ques!ons and type of test: For your selected sample, define two hypothesis ques!ons and the appropriate type of test hypothesis for each.
Address the following for each hypothesis:
a. Describe the popula!on parameter for the variable you are analyzing.
b. Describe your hypothesis in your own words.
c. Describe the inference test you will use.
i. Iden!fy the test sta!s!c.
4. Level of confidence: Discuss how you will use es!ma!on and conference intervals to help you solve the problem.
1-Tail Test
1. Hypothesis: Define your hypothesis.
a. Define the popula!on parameter.
b. Write null (Ho) and alterna!ve (Ha) hypotheses.
c. Specify your significance level.
2. Data analysis: Analyze the data and confirm assump!ons have not been violated to complete this hypothesis test.
a. Summarize your sample data using appropriate graphical displays and summary sta!s!cs.
i. Provide at least one histogram of your sample data.
ii. In a table, provide summary sta!s!cs including sample size, mean, median, and standard devia!on.
iii. Summarize your sample data, describing the center, spread, and shape in comparison to the na!onal informa!on.
b. Check the condi!ons.
i. Determine if the normal condi!on has been met.
ii. Determine if there are any other condi!ons that you should check and whether they have been met.
3. Hypothesis test calcula!ons: Complete hypothesis test calcula!ons, providing the appropriate sta!s!cs and graphs.
a. Calculate the hypothesis sta!s!cs.
i. Determine the appropriate test sta!s!c (t).
ii. Calculate the probability (p value).
4. Interpreta!on: Interpret your hypothesis test results using the p value method to reject or not reject the null hypothesis.
a. Relate the p value and significance level.
b. Make the correct decision (reject or fail to reject).
c. Provide a conclusion in the context of your hypothesis.
2-Tail Test
a. Hypotheses: Define your hypothesis.
1. Define the popula!on parameter.
2. Write null and alterna!ve hypotheses.
3. State your significance level.
b. Data analysis: Analyze the data and confirm assump!ons have not been violated to complete this hypothesis test.
a. Summarize your sample data using appropriate graphical displays and summary sta!s!cs.
i. Provide at least one histogram of your sample data.
ii. In a table, provide summary sta!s!cs including sample size, mean, median, and standard devia!on.
iii. Summarize your sample data, describing the center, spread, and shape in comparison to the na!onal informa!on.
b. Check the assump!ons.
i. Determine if the normal condi!on has been met.
ii. Determine if there are any other condi!ons that should be checked on and whether they have been met.
c. Hypothesis test calcula!ons: Complete hypothesis test calcula!ons, providing the appropriate sta!s!cs and graphs.
a. Calculate the hypothesis sta!s!cs.
i. Determine the appropriate test sta!s!c (t).
ii. Determine the probability (p value).
d. Interpreta!on: Interpret your hypothesis test results using the p value method to reject or not reject the null hypothesis.
a. Relate the p value and significance level.
b. Make the correct decision (reject or fail to reject).
c. Provide a conclusion in the context of your hypothesis.
e. Comparison of the test results: See Ques!on 3 from the Scenario sec!on.
a. Calculate a 95% confidence interval. Show or describe your method of calcula!on.
b. Interpret a 95% confidence interval.
Final Conclusions
1. Summarize your findings: Refer back to the Introduc!on sec!on above and summarize your findings of the sample you selected.
2. Discuss: Discuss whether you were surprised by the findings. Why or why not?
