Week 5 Project - STAT 3001 Student Name: Date: 11/7/17 VS This assignment is worth a total of 60 points. Part I. Chi-Square Goodness of Fit Test (equal frequencies) In order to determine staffing levels, a hospital wants to determine if births occur with the same frequency on each day of the week. The table below lists the days of the week selected by a random sample of 100 births. Consider the claim that the days of the week have the same frequency of a birth occurring. Sunday 32 Monday 16 Tuesday 7 Wednesday 20 Thursday 11 Friday 8 Saturday 6 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 1. Use the Chi-Square Goodness-of-Fit test to see if there is a difference between the frequency of births and days of the week. Use a significance level of .01. Paste results here. Num Categories: 400 Degrees of freedom: 399 Expected Freq: 0.4875 2. What are we trying to show 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. Test Statistic, X^2: 205.0000 Critical X^2: 467.6426 P-Value: 1.0000 Caution: Results may not be valid because one or more expected frequencies is less than 5. We are trying to show that each day of the week has the same chance / frequency for births. P value is 1.000___________________________ The goodness of fit of a statistical model describes how well it fits a set of observations. Measures of goodness of fit typically summarize the discrepancy between observed values and the values expected under the model in question. 1 5. Repeat the above procedure using only the weekdays Paste results here. Did you get different results? What do they mean? Part II. Chi-Square Goodness of Fit Test (unequal frequencies) In the 2000 U.S. Census, the ages of individuals in a small town were found to be the following: Less than 18 - 20% 18-35 - 30% and greater than 35 - 50% In 2010 the ages of 500 individuals from the same small town were sampled with the following results: Less than 18 - 121 people 18-35 - 288 people and greater than 35 - 91 people Using an alpha of 0.05, would you conclude that the population distribution of ages has changed in the last 10 years? 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 6. Complete the table as necessary. [Hint: You will need to compute the observed frequencies based on the percentages for the 500 samples. Round to the nearest integer.] 7. 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. 8. State the null and alternative hypothesis. Less than 18 121 OBSERVED EXPECTED 9. What conclusion would you reach, given the result of your Goodness-of-Fit test? [State in your own words following the guidelines for a conclusion statement learned 2 18-35 288 35-91 91 last week.] Part III. Chi-Square Test of Independence The following table is the result of a survey from a random sample of different crime victims. Use the data to test the claim that the type of crime is independent of whether the criminal was a stranger. Use a significance level of 0.05. Criminal was a stranger Criminal was an acquaintance or relative Homicid e 12 39 Robbery Assault 379 106 727 642 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 10. Just looking at the numbers in the table, what is your best guess about the relationship between type of crime and criminal being a stranger or not? Are they independent or is there a relationship? 11. Compute a Chi-Square Test of Independence on this data using a 0.05 level of significance. Paste your results here. 12. What are the null and alternative hypothesis for this test? 13. What is the p-value for this result? What does this represent? 14. 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: 3 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: 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