O'Halloran Final EDPSY 101 Section 002 HW Four(1)

EDPSY 101, Section 002: Analysis and Interpretation of Statistical Data in Education Final Homework Assignment for Spring 2024 ( 20 points ) Responses must be saved in Canvas (or submitted and confirmed as received by email attachment) by: May 1, 2024, 1pm ET Name: Breana O’Halloran Directions: Select the correct response for each multiple-choice item. Each multiple-choice item is worth 1 point. For the short-constructed response items, each response is worth 2 points. Show the calculation needed to construct the correct response for these items. 1. Which of the following is a large effect size for the coefficient of determination? D A. -.50 B. -.05 C. .01 D. .26 2. What is the null hypothesis to test: Does X predict Y? D A.  0    ¿   B.  0   ¿ 0 C.  0  β  ¿ β  D.  0  β ¿ 0 A research team studies whether time management skills predict academic productivity for undergraduate students. Please use the following SPSS results of simple linear regression to answer Questions 3 - 5 . Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1 .461 a .168 5.228 a. Predictors: (Constant), Time Management Coefficients Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta 1 (Constant) 74.654 4.338 17.211 .000 X .664 .302 .461 2.202 .041

a. Dependent Variable: Academic Productivity 3. Approximately, what percentage of variance in academic productivity is explained by time management skills? A A. 21.25% B. 30.58% C. 46.15% D. 55.39% 4. If X is equal to 0, then ^ Y is equal to which of the following values? D A. .664 B. 2.202 C. 17.211 D. 74.654 5. What statistical conclusion should the research team make? A. Time management skills are significantly different from academic productivity. B. Time management skills are not significantly different from academic productivity. C. Time management skills predict academic productivity significantly. D. Time management skills do not predict academic productivity significantly. 6. “The line of best fit” in simple linear regression minimizes the differences between: A. ρ and β . B. X and μ . C. α and p. D. Y and ^ Y .

Paired Samples Statistics Mean n Std. Deviation Std. Error Mean Pair 1 Week 1 80.03 30 7.117 1.299 Week 2 78.70 30 6.064 1.107 Paired Samples Test Paired Differences t df Sig. (2- tailed) Mean Std. Deviation Std. Error Mean 95% Confidence Interval of the Difference Lower Upper Pair 1 Week 1 – Week 2 1.333 3.745 .684 -.065 2.732 .061 9. What is the variance of the difference scores? Select the approximate answer with two decimal points? A. 13.15 B. 14.02 C. 15.81 D. 16.72 10. What is the t observed value that should be added in Table Two ? Calculate the approximate answer with two decimal points. (2 points) . Show your calculation for this item. (1.333) / sqrt of (3.745)^2 / 30 = 1.949 = 1.95

11. What statistical decision should the research team make about testing the null hypothesis? A. Fail to reject the null hypothesis because p value < .05 B. Fail to reject the null hypothesis because p value > .05 C. Reject the null hypothesis because p value < .05 D. Reject the mull hypothesis because p value > .05 Research Situation: A research team studies whether an online tutoring workshop can improve students’ academic writing skills. Forty students were randomly assigned to either the treatment condition (receiving the online tutoring) or the control condition (no online tutoring). A written composition test was given to students at the end of the semester. Research Question:

14. What is the t observed value? Calculate the approximate answer with two decimal points . (2 points) . A. 2.96 B. 2.57 C. 1.88 D. 1.24 15. What statistical conclusion should the research team make? A. There is no significant difference in mean writing scores between the two conditions. B. There is a significant difference in mean writing scores between the two conditions. C. There is no significant difference between the sample mean and the population mean. D. There is a significant difference between the sample mean and the population mean. Extra Credit Questions (2 points total, each item is worth 1 point). A research team studied how age predicts Internet usage. Please use the following scatter diagram with the line of best fit to answer Questions 16 - 17 .

16. Which of the following is most likely to be the simple linear regression equation of Internet usage predicted by age? A. ^ Y = 24.63 + 0.6X B. ^ Y = 24.63 – 0.6X C. ^ Y = 15.36 + 0.6X D. ^ Y = 15.36 – 0.6X 17. Four points are highlighted in the scatter diagram. Which point of A (red), B (green), C (blue), and D (orange) has the largest error of prediction? A. Point A B. Point B C. Point C D. Point D

Equations Simple linear regression equation: ^ Y = a + bX Slope: b = r XY ( S Y S X ) Intercept: a = Y − b X Coefficient of determination = r 2 Error of prediction = Y − ^ Y Independent samples t-test t observed = ( X 1 − X 2 ) √ ( S P 2 n 1 + S P 2 n 2 ) Pooled variance S p 2 = ( n 1 − 1 ) ( S 1 2 ) +( n 2 − 1 )( S 2 2 ) n 1 + n 2 − 2 Dependent samples t-test t observed = ¯ D √ S 2 D n