Jacky wanted to know if the mass body index (BMI) of a person affected his/her a

Question

Jacky wanted to know if the mass body index (BMI) of a person affected his/her ability to memorize information. She decided to examine 4 different groups based on BMI, including 5 participants with a very low BMI, 5 participants with a moderately low BMI, 5 participants with a moderate BMI, and 5 participants with a moderately high BMI, and 5 participants with a very high BMI (N = 20). From her data Jacky was able to determine the sum of squares (see below), but Jacky needs help finishing the independent-measures ANOVA. Using the information below, calculated both the observed F-value and the critical F-value (alpha of 0.05). N = 20 (note that you determine k) SSTotal = 40 SSWithin = 15 SSBetween = 25 F = 7.88, Fcritical (2,16) = 3.63 F = 7.88, Fcritical (3,16) = 3.24 F = 8.88, Fcritical (2,16) = 3.63 F = 8.88, Fcritical (3,16) = 3.24 F = 9.88, Fcritical (2,16) = 3.63 F = 9.88, Fcritical (3,16) = 3.24

Explanation / Answer

Given that, number of group ( k ) = 4, number of participants ( n ) = 5

Total number of participants ( N ) = 20

Significance level of alpha = 0.05

SSTotal = 40, SSWithin = 15, SSBetween = 25

Degrees of freedom (DF):

DFBetween = k - 1 = 4 - 1 = 3

DFTotal = N - 1 = 20 -1 = 19

DFWithin = DFTotal - DFBetween = 19 - 3 = 16

Now, Mean square ae,

MSBetween = SSBetween / DFBetween = 25/3 = 8.3333

MSWithin = SSWithin / DFWithin = 15/16 = 0.9375

F-value = MSBetwee / MSWithin = 8.3333 / 0.9375 = 8.88

Critical-F value is F(3, 16) = 3.24

Therefore, Fcritical = 3.24 , F = 8.88

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