Part 3: Due Monday, December 5, 2022
Use the same research topic that you chose in week 1. Also use the data that you collected during week 1. If you need to change or supplement (i.e. add new data) the data set for this assignment, you may.
Create a document answering all the questions below. Save your work and submit on Canvas.
This part of the project will be worth 200 points, double the value of the first two parts.
You have collected data from a sample of at least 50 elements in your population. But what information would you like to know about the entire population? Would you like to know the mean home price of all properties in your area?
Write 2 paragraphs briefly summarizing the data that you collected from the sample and the information that you would like to INFER about the population.
Choose 2 sample statistics from your data, one PROPORTION and one MEAN. Try to use variables that you mentioned in question 1 concerning inference. For example, You might choose the mean sales price of a home.
Estimate the population parameters by first computing point estimates from your sample data. Then:
Construct and interpret a 90% confidence interval for the population proportion.
What sample size would be necessary to estimate the proportion with a 2% margin of error and a 90% confidence?
Construct and interpret a 95% confidence interval for the population mean.
Do you think that your sample of size 50 is large enough? Why or why not?
Next, you will be conducting one hypothesis test. Without considering the specific values of your sample statistics, make a conjecture (hypothesis) about one of the variables you used for the confidence intervals above.
Matt claims that the proportion of homes with 3 or more BRs in Fairfax county is less than 0.4.
1-State the null and alternative hypotheses using mathematical symbols.
2-Is this a one-tailed or a two-tailed test?
3-State the level of significance.
This will be α ＝ 0.05 for everyone.
4-Compute the test “test statistic.” You are encouraged to use Statcrunch.
5-Use probability tables (z or t, as required) or statistical software to determine the p-value.
6-Compare the p-value with the level of significance
7-State the conclusion of the hypothesis test. The conclusion should include the phrases “Reject the null” or “Fail to reject the null” as well as a statement in practical language.
In addition to performing the hypothesis test above, write 1-2 paragraphs explaining the relationship between your hypothesis test and the confidence interval from your Task #1. Also discuss what it would mean had you made a Type I or a Type II error in the hypothesis test.
Finally, write no more than one page summarizing your entire project. (Double spaced, 12-point font, 1 inch margins.) What did you think of the research project? Did the statistical analysis help you learn more about the topic? For example, you could address the following:
Is there any home on your list that seems like a good value?
How much should you plan on spending on a home in your desired area?