Question

I need to develop an ANOVA table for the following descriptive statistics for 3 different brands of flower seeds to determine the number of seeds out of 100 that will sprout

brand 1 n-5 S2-275 xbar-85

brand 2 n-5 S2- 337.5 xbar-54

brand 3 n-5 S2=312.5 xbar-52

Answer 1

Calculations For the ANOVA Table:

Overall Mean = [(5 * 85) + (5 * 54) + (5 * 52)]/15 = 63.67

SS treatment = SUM n* ( x̅_i - overall mean)² = 5 * (85 - 63.67)² + 5 * (54 - 63.67)² + 5 * (52 - 63.67)² = 3423.33

df1 = k - 1 = 3 - 1 = 2

MSTR = SS treatment/df1 = 3423.33 / 2 = 1711.67

SSerror = SUM [(n - 1) * Variance] = 4 * 275 + 4 * 337.5 + 4 * 312.5 = 3679.79

df2 = N - k = 15 - 3 = 12

Therefore MS error = SSerror/df2 = 3679.79/12 = 308.15

F = MSTR/MSE = 1711.67/308.15 = 5.56

The ANOVA table is as below.

Source	SS	DF	Mean Square	F
Between	3423.33	2	1711.67	5.56
Within/Error	3697.79	12	308.15
Total	7121.12	14