Correlation Homework

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Clemson University *

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3300

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Statistics

Date

Feb 20, 2024

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pdf

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Uploaded by ElderBraveryHummingbird16

Correlation Homework You are interested in whether there is a relationship between happiness and the number of friends an individual has on Facebook. Happiness is measured on a scale of 1 to 50 (1- unhappy, 50-extermely happy). You measure 10 individuals. Their scores are below. Round to 3 decimal points. Assume 𝛂 =0.05. ID Happiness Facebook Friends 1 42 537 2 39 485 3 40 486 4 48 673 5 40 468 6 41 501 7 41 620 8 29 309 9 38 415 10 37 385 1. What is your Null Hypothesis? (1) Ho: r=0 2. What is your Alternative Hypothesis? (1) Ha: r ≠ 0 3. Is this a one-tailed or two-tailed test? (1) two tailed 4. What is your total df (for finding your critical t)? (1) 8 5. Report the critical t. (1) 2.306 and -2.306 6. Fill in the table on the back. (12) 7. Report r. (2) 0.935 8. Compute t. (2) 7.45 9. Write a “Given…” statement (including computed and critical t). (3) Given our sample, since our computed t (7.54) was more extreme than our critical t (2.306), we reject our Ho and favor our Ha 10. Interpret r. (What does this say about happiness and Facebook friends?) (1) There is a strong linear correlation between happiness and number of Facebook friends. 11. Report r 2 . (2) .874 12. Interpret r 2 . (3) Approximately 87.4% of the variation in happiness can be explained by number of Facebook friends. 13. Enter the table (as it appears) above in SPSS. 14. Click “ Graphs ” → “ Legacy Dialogs ” → “Scatter/Dot…” → Select “Simple Scatter” and click “Define”. Enter “Happiness” on the “Y Axis ” and

“Facebook_Friends” on the “X Axis ”. Click “OK” to run the scatterplot. 15. Does your scatterplot fit your interpretation of r? (1) The scatterplot shows that it is a positive correlation, but it is not a strong linear correlation. 16. Now click “ Analyze ” → “Correlate” → “Bivariate…”. Move your two variables (Happiness and Facebook Friends) into the “Variables” box and click “OK”. 17. Print and attach your Output window. (5)

Facebook Friends Happiness X X-M (X-M) 2 Z X Y Y-M (Y-M) 2 Z Y Z X Z Y 42 2.5 6.25 1.319 537 49.1 2410.81 22.578 29.780 39 -.5 .25 .053 485 -2.9 8.41 .079 .004 40 .5 .25 .053 486 -1.9 3.61 .034 .087 48 8.5 72.25 15.243 673 185.1 34262.01 320.877 4891.128 40 .5 .25 .053 468 -19.9 396.01 3.709 .197 41 1.5 2.25 .475 501 13.1 171.61 1.607 .763 41 1.5 2.25 .475 620 132.1 17450.41 163.43 77.629 29 -10.5 110.25 23.259 309 -178.9 32005.21 299.742 6971.699 38 -1.5 2.25 .475 415 -72.9 5314.41 49.772 23.642 37 -2.5 6.25 1.319 385 -102.9 10588.41 99.165 130.799 ∑ = 395 ∑(X -M) 2 = 202.5 ∑ = 4879 ∑(Y -M) 2 = 102610.9 ∑(Z X Z Y ) = 12125.728 M=39.5 S 2 = 22.5 M=487.9 S 2 = 11401.211 r = .935 S = 4.74 S = 106.776

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