Cumulative Worksheet KEY(1)

Cumulative Worksheet KEY PSYC 1303, Spring 2023 Note: Make sure that you know the formulas we have used throughout our class lectures, worksheets, quizzes, and exams thus far. Memorizing the formulas will make the final a substantially smoother experience. On this worksheet, round all answers to the nearest tenths place (e.g., 4.662 would round to 4.66). 1. A student’s raw score on Midterm 2 is 77. The mean from the class is 82. What is this student’s distance from the mean? What is the student’s deviation? Distance from the mean: 5 Deviation: -5 2. A researcher noted the ages of people taking the Greyhound bus from Los Angeles to San Diego over a one-week period. Complete the frequency table for this variable. Ages of People on Greyhound Bus Width of Interval Frequency (Number of People) Percent in Interval Density (Percent per Unit) 0 to 11 11 10 13.51% 1.22% 12 to 18 6 10 13.51% 2.25% 19 to 24 5 25 33.78% 6.76% 25 to 50 25 17 22.97% 0.92% 51 to 75 24 12 16.22% 0.68% TOTAL 74 100% 3. Construct a density histogram based off of the table in Problem 2. Email Professor Ziencina to check your work on this.

4. Fill out the table below, calculating the standard deviation (SD). Raw Score Deviation Squared Deviation 12 -16.90 285.61 51 22.10 488.41 9 -19.90 396.01 14 -14.90 222.01 76 47.10 2218.41 13 -15.90 252.81 4 -24.90 620.01 5 -23.90 571.21 23 -5.90 34.81 82 53.10 2819.61 Mean 28.90 0 790.89 Standard Deviation 28.12 5. Fill out the table below, calculating the standard deviation and z-scores. Raw Scores Deviations Squared Deviations z-Scores 8.00 -1.00 1.00 -0.34 12.00 3.00 9.00 1.01 13.00 4.00 16.00 1.35 6.00 -3.00 9.00 -1.01 6.00 -3.00 9.00 -1.01 Sum 45.00 0 44.00 0.00 Mean 9.00 0 8.80 0.00 SD 2.97 0.00 6. The following two points are on a line: (4, 7) and (10, 12). a. Calculate the slope.

SD 6.0 9 4.66 9. Use the raw data for X and Y below to calculate the SDs, z-scores, and correlation coefficient. Then, answer questions a through d for the regression line that fits this raw data. Note: There may be slight differences in your answers due to differences in rounding while performing the calculations. raw scores deviations squared deviations z-scores cross-products x y x y x y z x z y 8 5 1.29 1.43 1.65 2.04 0.31 0.63 0.20 2 1 -4.71 -2.57 22.22 6.61 -1.15 -1.14 1.31 4 6 -2.71 2.43 7.37 5.90 -0.66 1.08 -0.71 14 2 7.29 -1.57 53.08 2.47 1.78 -0.70 -1.24 10 7 3.29 3.43 10.80 11.76 0.80 1.52 1.22 2 3 -4.71 -0.57 22.22 0.33 -1.15 -0.25 0.29 7 1 0.29 -2.57 0.08 6.61 0.07 -1.14 -0.08 sum 47 25 0.00 0.00 117.43 35.71 mean 6.71 3.57 0.00 0.00 16.78 5.10 SD 4.10 2.26 r 0.14 a. What is the standardized regression equation for the data in the table above? ^ z Y = .14 * z x b. What is the unstandardized slope? r ∗ SD Y SD X = .14 ∗ 2.26 4.10 = .08 c. What is the unstandardized intercept? slope = .08 point of averages (using raw scores) = (6.71, 3.57) general formula for a line: y = b * x + a substitute and solve: 3.57 = .08 * 6.71 + intercept 3.57 = .54 + intercept

3.03 = intercept d. What is the unstandardized equation of the regression line? y = .08 * x + 3.03 10. You are running a study that seeks to examine how many U.S. teens engage in illegal behavior. You conduct 2000 surveys of 100 participants each across the U.S., and you calculate the proportion of teens who have engaged in some kind of illegal activity (e.g., shoplifting, driving without a license). The average of the proportions from the 2000 samples is .77; the standard deviation is .24. a. What is the sample? 200,000 U.S. teens b. What is the population? All teens in the U.S. c. What is k? 2000 d. What is N? 100 e. What is E(p)? .77 f. What is pi? .77 g. What is SE p ? .24 11. In the state of Texas, 67% of household have a dog. 1000 surveys were conducted throughout the state, with 100 people in each sample. Answer the questions below to find the 95% CI for p around pi. a. What is the expected value of p?

.44 d. What is the estimated value of sigma? .50 e. What is the standard error? .01 f. Construct a 95% CI for pi around p. 95% CI: (.42, .46) g. Is it likely that 45% of adults in Connecticut suffer from anxiety? How do you know? Yes; .45 is contained within the 95% CI 13. Another researcher finds that the average time spent walking outside daily among 1000 young adults randomly selected from across Texas is 36 minutes. The standard deviation is 5.5 minutes. a. What is N? 1000 b. What is X ? 36 c. What is the SD? 5.5 d. For the above sampling distribution of the mean, calculate SE X . .17 e. Construct a 95% CI for μ (the population mean). (35.66, 36.34)

f. Is it likely that the average time spent walking among all young adults in Texas is 30 minutes? How do you know? No; 30 is not contained within the 95% CI 14. You decide to compare time spent watching TV among younger and older college students. Each group consists of 300 people. The younger college student group reports an average of 11 hours of TV watched per week, with a standard deviation of 0.22 hours. The older college student group reports an average of 7 hours of TV watched per week, with a standard deviation of 0.41 hours. You also find that the standard error of the difference between means is 0.37. a. What is X 1 − X 2 ? 11 – 7 = 4 OR 7 – 11 = -4 b. What is E( X 1 − X 2 )? 0 c. What is SE X 1 − X 2 ? 0.37 d. What it the t -statistic value? 4/0.37 = 10.81 OR -4/0.37 = -10.81 e. The critical region includes the 5% of the least likely t -scores. Does the value of t fall within the critical region? How do you know? Yes; 10.81 is greater than the critical value or 2 OR Yes; -10.81 is less than the critical value of -2 f. Based on this t -score, should you reject the null hypothesis or fail to reject (aka “accept”) the null hypothesis? Reject the null hypothesis g. Suppose that you decided to reject the null hypothesis, but the null hypothesis was actually true. What kind of error (i.e., Type I or Type II) would you have committed? Type I error