Applied Statistics Problems

Part I For years, researchers have used random digit dialing to collect data. However, random digit dialing surveys do not call cell phones, and increasingly people are using cell phones only. If the opinions of people who have only cell phones differ from those with landline service (this includes those with and without cell phones), the poll results from random digit dialing surveys may not represent the entire population. The Pew Research Center conducted a random sample of 200 adults to see if there is a difference between cell-only and landline users in terms of their political party preference. The results are shown in the cross-tab below. Party Preference Phone Use Cell-phone only Landline use Total Democrat or Lean Democrat 57 60 117 Republican or Lean Republican 39 44 83 Total 96 104 200 1. Calculate Yule’s Q for the cross-tab above. Show all your work 2. Calculate chi-square for the cross-tab above. Show all your work 3. Change the frequencies in the cross-tab to percentages 4. In a paragraph (at least 6-7 sentences), discuss the results above. What do Yule’s Q and the percent distribution in the cross-tab tell you about the relationship between phone use and political party affiliation? Is there a statistically significant relationship between these variables? Be specific in your answer and make certain to reference the statistics calculated in questions #1-3 Part II Several years ago, the City of Mesa created a screening program for all applicants for city jobs, and a team of city administrators screened applicants for their suitability for employment (1=lowest, 20=highest). Now, this program is being evaluated, and the actual work performance of a sample of hired employees is being rated (0=lowest, 100=highest). Employee Applicant Screening Score Employee Performance Evaluation A 19 82 B 18 88 C 17 85 D 15 95 E 14 77 F 13 72 G 12 71 H 11 75 I 10 92 J 9 65 K 8 32 L 7 55 M 5 21 N 4 45 O 2 25 1. Calculate Spearman’s rho (rs) for the data above. Show all your work 2. Is there a relationship between the original screening score for applicants and employee work performance? What does the direction of the relationship between the variables tell you? In a paragraph (at least 4-5 sentences), based on the results from the correlation, what do you tell city administrators? Should the screening process be continued? Why or why not? Part III State election officials feel that voter turnout for local elections is influenced by the unemployment rate within the city. Specifically, officials feel that a high unemployment rate will reduce voter turnout. Previous studies have indicated that higher unemployment rates produce fewer voters because of decreased resources, alienation, and distraction due to personal problems. Officials have gathered information from 5 different cities on the percentage of registered voters who actually voted in the most recent local election and the city’s unemployment rate. City Unemployment Rate (%) Turnout (%) A 5 55 B 8 60 C 9 65 D 9 68 E 10 70 1. Calculate Pearson’s r for the data above. Show all your work 2. Is there a relationship between unemployment rates and voter turnout? What does the direction of the relationship between the variables tell you? In a paragraph (at least 4-5 sentences), based on the results from the correlation, what do you tell election officials?(1 point). 3. What is the coefficient of determination (r 2 ) for the data? What does that tell you about the relationship between these two variables? Part IV The U.S. Postal Service is attempting to reduce the number of complaints made by the public against its workers. In order to facilitate this task, a staff analyst for the service regresses the number of complaints lodged against an employee last year on the hourly wage of the employee for the year. The regression equation finds: Y = 20.2 – 1.2X with a r 2 of .73 1. What is the IV? What is the DV? 2. If wages were increased by $1.00, what is the expected effect on the number of complaints received per employee? How can you tell? 3. The average starting hourly salary for USPS is $9.00. If an employee earns the average starting salary wage, how many complaints can that employee expect to receive?