I was interested in determining whether differences in cognitive ability exist between children (Group 1), adults (Group 2), and the elderly (Group 3). I gave all three groups the same memory test (score out of 100) and below are the data.

Group 1 Group 2 Group 3

mean 24 94 89

n 20 20 20

SS WITHIN = 250

SS TOTAL = 950

Please fill in the ANOVA summary Table below and write up your results. Do not forget to indicate the null and alternative hypotheses. **HINT** Draw a matrix if you feel that will help. 

Source of Variation df SS MS F

3) A researcher is interested in examining the relationship between self-esteem and work productivity. She believes that a person with higher self-esteem will be a more productive worker. She gave a random sample of workers at a major corporation a self-esteem inventory and also assessed their work productivity. The self-esteem inventory called the NSP was measured on a 1-5 scale with lower scores indicating lower self-esteem. The worker productivity was measured on a 1-10 scale with lower scores indicating lower productivity. Assess the relationship between self-esteem and work productivity using the appropriate analysis, including your hypotheses, the critical value. Show your work and provide a brief conclusion. 

SE (X) Prd (Y) XY X² Y²

2 7 14 4 49

1 9 9 1 81

3 6 18 9 36

4 5 20 16 25

5 4 20 25 16

2 7 14 4 49

2 6 12 4 36

5 3 15 25 9

3 4 12 9 16

2 8 16 4 64

29 59 150 101 381

4). Define the central limit theorem and explain why bunny rabbit weight is a useful example to understand the central limit theorem.