Week 5 Project - STAT 3001 Student Name: Date: This assignment is worth a total of 60 points. Part I. Chi-Square Goodness of Fit Test (equal frequencies) For a recent year the number of homicides that occurred in New York City are given in the table below. Use a 0.05 level of significance to test the claim that the homicides in NYC are equally likely to occur in each of the 12 months. Ja n 38 Fe b 30 Mar Ap r 46 40 Ma y 46 Ju n 49 Jul 47 Au g 50 Sep Oct No v 50 42 37 Dec 37 Instructions for performing this test in Stat Disk can be found in the Stat Disk User's Manual under Goodness of Fit, Equal Frequencies. Instructions Answers Use the chi squared goodness of fit test to see if there is a difference between the frequencies of homicides in different months. Use a significance level of 0.05 and past the results here: 1. 2. What are we trying to show here? Use the chi squared goodness of fit test to see if there is a difference between the frequencies of homicides in different months. Use a significance level of 0.05 and past the results here: 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 the summer months of Jun through Sep. Paste results here. Did you get different results? Would these results support the police commissioner's claim that more homicides occur in the summer when the weather is nicer. 1 Part II. Chi-Square Goodness of Fit Test (unequal frequencies) Acme Toy Company prints baseball cards. The company claims that 30% of the cards are rookies, 60% veterans, and 10% are All-Stars. Suppose a random sample of 100 cards has 50 rookies, 45 veterans, and 5 All-Stars. Is this consistent with Acme's claim? Use a 0.05 level of significance. Instructions for performing this test in Stat Disk can be found in the Stat Disk User's Manual under Goodness of Fit, Unequal Frequencies. Instructions Answers 1. Complete the table as necessary. [Hint: You will need to compute the observed frequencies based on the percentages for the 100 samples. Rookies OBSERVED 50 EXPECTED 2. Use the Chi-Square Goodness-of-Fit test for Unequal Frequencies to see if there is a difference between the observed frequencies and the expected frequencies Use a significance level of .05. Paste results here. 3. State the null and alternative hypothesis. 4. What conclusion would you reach, given the result of your Goodness-of-Fit test? Does the data support the company's claim?[State in your own words following the guidelines for a conclusion statement learned last week.] Part III. Chi-Square Test of Independence 2 Veterans 45 All-Stars 5 A randomized controlled trial was designed to compare the effectiveness of splinting versus surgery in the treatment of carpal tunnel syndrome. Results are given in the table below. Use a significance level of 0.01 to test the claim that success is independent of the type of treatment. Splint treatment Surgery treatment Successful 60 67 Unsuccessful 23 6 Hint: Instructions for performing this test in Stat Disk can be found in the Stat Disk User's Manual under the heading Chi Square Test of Independence (Contingency Tables). Instructions Answers 5. Just looking at the numbers in the table, what is your best guess about the relationship between type of treatment and success? Are they independent or is there a relationship? 6. Compute a Chi-Square Test of Independence on this data using a 0.01 level of significance. Paste your results here. 7. What are the null and alternative hypothesis for this test? 8. What is the p-value for this result? What does this represent? 9. State your conclusion related to the context of this problem. 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: Do not use this problem!! 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: 3 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 We have evidence to believe .... 15 Submit your final draft of your Word file by going to Week 5, Project, and follow the directions under Week 5 Assignment 2. Please use the naming convention "WK5Assgn2+first initial+last name" as the Submission Title. 4