Week 5 Project - STAT 3001 Student Name: Lawante Bryant-Scott Date: 6-29-2015 This assignment is worth a total of 60 points. Part I. Chi-Square Goodness of Fit Test (equal frequencies) Four different brands of a pain medication used for chronic back ailments were tested to see if the number of side effects for each brand were the same. The table below lists the results of the reported number of side effects for each brand of pain medication. Brand A 23 Brand B 17 Brand C 33 Brand D 11 [Hint: Be sure to watch the video at Week 5 Resources on the \"Chi-Square Goodness-of-Fit test (equal frequencies)\" before attempting this problem. Instructions for performing this test in STATDISK can be found in the Statdisk User Manual.] Instructions Answers 1. Use the Chi-Square Goodness-of-Fit test to see if there is a difference between the number of side effects from the different brands of medication. Use a significance level of .01. Paste results here. 2. What are we trying to show here? Num Categories: 4 Degrees of freedom: 3 Expected Freq: 21 3. What is the p-value and what does it represent in the context of this problem? 4. State in your own words what the results of this Goodness-of-fit test tells us. 5. Repeat the above procedure using only Brands A, B, and D. Paste results here. The p-value is 0.0057 and it represents that there is substantial evidence against the null hypothesis that Test Statistic, X^2: 12.5714 Critical X^2: 11.34488 P-Value: 0.0057 Num Categories: Degrees of freedom: Expected Freq: 3 2 17 Test Statistic, X^2: 4.2353 1 Critical X^2: P-Value: 6. Do you get a different result? Yes 2 9.210334 0.1203 Part II. Chi-Square Goodness of Fit Test (unequal frequencies) An opinion poll was taken to see how people felt about Health Care reform. Previous poll results indicate that within a particular population 34% were for reform, 41% were against reform, and 25% were uncertain. This year, the following results were observed: FOR: 317 people AGAINST: 223 people UNCERTAIN: 211 people [Hint: Be sure to watch the video at Week 5 Resources on the \"Chi-Square Goodness-of-Fit test (unequal frequencies)\" before attempting this problem. Instructions for performing this test in STATDISK can be found in the Statdisk User Manual.] Instructions Answers 7. Complete the table as necessary. [Hint: You will need to compute the expected frequencies based on the previous poll results. Round to the nearest integer.] OBSERVED EXPECTED 8. Use the Chi-Square Goodness-of-Fit test for Unequal frequencies to see if there is a difference between the observed frequencies (this year) and the expected frequencies (based on the previous poll results). Use a significance level of .01. Paste results here. 9. State the null and alternative hypothesis. 10. What conclusion would you reach, given the result of your Goodness-of-Fit test? [State in your own words.] 3 Part III. Chi-Square Test of Independence A study was done to test the claim that discharging a newborn infant discharged early (less than 30 hours after birth) is related to re-hospitalization of that infant within a week of discharge. The following data was collected related to early discharge and re-hospitalization: Early Discharge (less than 30 hours) Late Discharge (30 - 78 hours) Re-hospitalized within 1 week 622 631 Not re-hospitalized 3997 4660 Total 4619 5291 Hint: Instructions for performing this test in STATDISK can be found in the Stat Disk User's Manual under the heading Chi Square Test of Independence (Contingency Tables). Instructions Answers 11. Just looking at the numbers in the table, what is your best guess about whether early discharge is related to re-hospitalization? [Hint: you might compute the difference in percentages between those that were discharged early and those that were not.] 12. Compute a Chi-Square Test of Independence on this data using a 0.05 level of significance. Paste your results here. 13. What is the null and alternative hypothesis for this result? 14. What is the p-value for this result? What does this represent? 15. State your conclusion related to the context of this problem. 4 Part IV. Apply this to your own situation Using one of the above statistical tests, compose and SOLVE an actual problem from the context of your own personal or professional life. You will need to make up some data and describe which test you will use to analyze the situation. Here's an example: Example State the problem that you are analyzing. Make up some data for the new situation. Last year, I asked the kids in my neighborhood what kind of cookies they preferred. 50% said chocolatechip, 20% said oatmeal-raisin, and 30% said sugar cookie. I want to see if this has changed. I asked 50 neighborhood kids what kind of cookie they preferred now and here's what they said: Determine which type of Chi-Square test you will perform. Specify your null and alternative hypotheses. Setup the test 35 said chocolate-chip 5 said oatmeal-raisin 10 said sugar-cookie Since these are unequal frequencies, I will perform a Chi-Square Goodness-of-Fit Test (Unequal Frequencies). H0: There is no difference this year in the preferences of cookies within the neighborhood kids. H1: Things have changed. Chocolate OatmealSugar-Chip Raisin Cookie OBSERVED 35 5 10 EXPECTED 25 10 Perform the test Paste your STATDISK results here State your conclusion 15 We have evidence to believe .... Submit your final draft to the Assignment 2 Turnitin - Week 5 area of your course. Please use the naming convention "WK5Assgn2+first initial+last name" as the Submission Title. 5