Question

Fifteen people are randomly assigned, so that 5 people exercise in the morning, afternoon, or night. After 8 weeks, their weight loss is measured in pounds. Compute SSwithin.

SS morning (EXmorning) morning n (EX afternoon) SS afternoon afternoon n (EXnight) SS night night n SS within(error) = SS morning + SS afternoon + SS night Morning Afternoon Night Morning? 100 Afternoon2 64 Night2 10 8 6 36 8 64 8 64 7 49 7 49 9 81 5 25 5 25 7 49 4 16 9 81 7 49 5 25 EXmorning = 39 Exmorning = 319 EX afternoon = 39 afternoon Mmorning = 7.8 Mafternoon = 7.8 = 307 EXnight = 27 Exnight = 151 Mn night = 5.4 (EXnight)2 = 729 (EXmorning)2 = 1,521 (EX afternoon)2 = = 1,521

A. 3,719.2

B. 22.8

C. 3,615.6

D. 525.6

Can you please show me how you get your answer? I'm writing it out and I keep getting 525.6 but I keep being told that it's wrong. Thank you!

Answer 1

Let the $\sum$ = SUM

SS morning = SUM(X² morning) - SUM(X morning)²/n = 319 - (39)²/5 = 319 - (1521 / 5) = 319 - 304.2 = 14.8

SS afternoon = SUM(X² afternoon) - SUM(X afternoon)²/n = 307 - (39)²/5 = 307 - (1521 / 5) = 307 - 304.2 = 2.8

SS night = SUM(X² night) - SUM(X night)²/n = 151 - (27)²/5 = 151 - (729 / 5) = 151 - 145.8 = 5.2

Therefore SS within = SS morning + S afternoon + SS night = 14.8 + 2.8 + 5.2 = 22.8

Option B