Mathematics Homework Help

Task #1

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?  Would you like to know the average starting salary of all graduates who have completed 4 years of college? Etc.

1. 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.
2. 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 may choose the proportion of people who graduate with student loans of more than $10,000.  You might choose the mean sales price of a home.
3. Create interval estimates for the two population parameters that correspond to the sample statistics chosen above.     
   1. PROPORTION         
      • Construct and interpret a 90% confidence interval for the population proportion.
      • What sample size would be necessary to estimate the proportion with a 4% margin of error and a 95% confidence?
   2. MEAN         
      • 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?

Task #2

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.

For example: 

• Matt claims that the average salary of a worker with a college degree will be greater than $92,000.
• 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.     
   • Is this a one-tailed or a two-tailed test?
2. State the level of significance.     
   • This will be ? = 0.05 for everyone.
3. p-value Approach     
   1. Compute the test “test statistic.”
   2. Use probability tables (z or t, as required) or statistical software to determine the p-value.
   3. Compare the p-value with the level of significance
   4. 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 of interpretation 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.

Task #3

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:

1. HOME VALUES     
   1. Is there any home on your list that seems like a good value?
   2. How much should you plan on spending on a home in your desired area?
2. BENEFITS OF COLLEGE     
   1. Do you believe there is a financial benefit to attending college?
   2. What is the short-term and long-term benefits of your education choice?