PSYC 2317 Take Home Test #2 1) The local little league baseball team needs your help. Their season lasts 2 months over the summer. The second month of each season, the kids sell team t-shirts to fans as a way of earning money to support the team. It costs some money to print the shirts, so they don't want to print too many (that drives costs up) or print too few (they miss out on sales). They ask you to figure out a way to predict what the demand will be for t-shirts so they can print the correct number. You ask the team to provide you data for each of the last 15 seasons (shown below). Based on the data provided, which of the 3 possible predictor variables (X1, X2, or X3) should you use to predict the number of t- shirts the team is likely to sell next season? Assume you may only pick one predictor variable. Provide statistical calculations to back up your choice of predictor variable. Predictor - X1 # games won 1st month of season Predictor - X2 # of radio ads 1st month of season Criterion - Y Predictor - X3 Average attendance # t-shirts sold 1st month of season that season It is in the direction you would expect between how many years a person has owned their car, and the current value of their car. NOTE: In case you don't know, cars always decrease in value as time goes on. In fact, a new car decreases in value several thousand dollars the moment the new owner drives it off the dealer's lot. . It is the weaker correlation. +.19 -.24 +.20 -.22 +.13 14 12 425 231 9 11 378 211 13 5 456 248 12 10 354 190 6 6 390 175 16 8 423 207 12 9 412 233 9 384 195 9 7 436 200 9 10 453 218 15 12 411 250 10 9 427 235 8 5 406 213 16 10 394 245 14 11 460 230 2) Using only the single predictor variable you chose as your answer to the previous problem, predict how many t-shirts the team should print this season if during the 1st month of this season they won 13 games, broadcast 8 radio ads, and had an average attendance of 437. 3) Calculate the standard error of the estimate for the method you used to predict how many t-shirts the team should print. Does your answer indicate that is how much error you had when you made your prediction (for question #2) about how many t-shirts the team should print this season? Explain why or why not. 5) You work as a data analyst for the mayor of a small city. The mayor wants to keep the taxes low in your city, but she needs to find a way to generate income to pay for all the city services. The mayor is thinking about increasing the number of speed traps (the city currently has 4 speed traps set up) along the interstate highways that pass through your city. She figures the traffic speeding through the city should provide plenty of income in the form of speeding tickets. The only problem is that more speed traps takes officers away from other policing responsibilities; therefore, the increase in revenue from speed traps would need to be significant enough to justify this use of policing time and resources. The mayor talks to the police chief and the chief says he will look over historical records to see if increasing the number of speed traps is a good idea. The police chief uses the monthly data for the last 2 years (shown below) and calculates a Pearson-r correlation of 0.05 between the number of speed traps and how much income they generated for the city. . Based on the Pearson-r value, would the mayor's idea of increasing the number of speed traps likely generate enough extra income to justify the use of police time or not? Explain why or why not. Did the police chief analyze the data properly or did he neglect to do something that would have changed how he approached analyzing the data? In other words, was the Pearson-r the appropriate statistic to use? If you think he neglected something, explain what it is and describe the effect it would have on the decision to use more speed traps. # of speed traps that month Ticket revenue that month 4 $12,732 7 $19,368 10 $17,523 3 $7,320 $17,942 4) Which of the following correlation coefficients (shown in the table below) meets BOTH the criteria shown below? Explain how you determined which answer to pick. 11 $11,213 $21,364 6 $18,658 $15,563 10 $14,624 8 $25,455 9 $15,980 $15,755 7 11 $14,877 10 7 $18,940 $20,541 $13,422 10 $13,850 9 $17,489 8 $23,784 5 $14,980 8 $24,866 11 $12,365 $18,750 6) You are listening to a politician who is giving an interview on a talk show. The politician is arguing that local public schools should change how they teach math. The politician says the public schools should model their math instruction after the methods used by local private schools because the private school instruction methods work better. The interviewer asks how the politician knows the private school instruction methods are better. The politician points to a recent study of local area schools. In the study, researchers gathered a sample of 450 school children all from the 5th grade. They measured which type of school a child currently attended (public or private) and how well each child did on a standardized state test at the end of the 5th grade (i.e., all the kids took the same test). Results showed that the average test score for the 5th graders in the private schools (n = 225) was 84%; whereas, the average result for 5th graders in the public schools was 71% (n = 225). Does this evidence clearly indicate that the teaching methods used by private schools to teach math are more effective than what the public schools do? If yes, explain why. If no, explain why not. 7) Below is data showing how many minutes some students from Timmy's class studied for their spelling test and what score they earned on the test. Use this data do the following: Create a scatterplot of the data Calculate the regression equation for using # of minutes studied to predict test score Draw the regression line in your scatterplot precisely where it should go (i.e., based on plotting it, not estimating its location). NOTE: You need to show how you determined where two points are on the regression line, so I see how you figured out where to draw the line. # Minutes Studied Test Score 20 71 21 84 35 84 15 68 20 77 31 94 15 73 27 82 10 76 17 83