For each of the following situations, give the degrees of freedom for the group
ID: 2946760 • Letter: F
Question
For each of the following situations, give the degrees of freedom for the group (DFG), for error (DFE), and for the total (DFT). State the null and alternative hypotheses, H0 and Ha, and give the numerator and denominator degrees of freedom for the F statistic.
(a) A poultry farmer is interested in reducing the cholesterol level in his marketable eggs. He wants to compare two different cholesterol-lowering drugs added to the hen's standard diet as well as an all-vegetarian diet. He assigns 30 of his hens to each of the three treatments.
denominator df =
denominator df =
denominator df =
DFG = DFE = DFT =Explanation / Answer
DFG is given by the number of columns - 1, DFE = Total sample size - number of columns and DFT = DFG + DFE
The df Numerator = DFG and df denominator = DFE
(a) Number of columns = number of treatments = 3
Total sample size = 90 (30 hens for each treatment)
DFG = 3 - 1 = 2
DFE = 90 - 3 = 87
DFT = 87 + 2 = 89
df numerator = DFG = 2
df denominator = DFE = 87
(b) Number of columns = number of categories = 3
Total sample size = 95
DFG = 3 - 1 = 2
DFE = 95 - 3 = 92
DFT = 92 + 2 = 94
df numerator = DFG = 2
df denominator = DFE = 92
(c) Number of columns = number of tgroups = 3
Total sample size = 42
DFG = 3 - 1 = 2
DFE = 42 - 3 = 39
DFT = 39 + 2 = 41
df numerator = DFG = 2
df denominator = DFE = 39
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