For each of the following situations, give the degrees of freedom for the group

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, Ho 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 25 of his hens to each of the three treatments DFG DFE- DFT 0 O The all-vegetarian diet group has a higher mean cholesterol level O The all-vegetarian diet group has a lower mean cholesterol level. O At least one group has a different mean cholesterol level O All groups have the same mean cholesterol level. OAll groups have different mean cholesterol levels O All groups have different mean cholesterol levels O At least one group has a different mean cholesterol level O All groups have the same mean cholesterol level. O The all-vegetarian diet group has a higher mean cholesterol level O The all-vegetarian diet group has a lower mean cholesterol level numerator df denominator df

Explanation / Answer

a)

DFG =k-1=2

DFE =N-k =75-3=72

DFT =74

Ho: all groups have the same mean cholestrol level

Ha: at least one group has a different mean cholestrol level

numerator df =2

denominator df =72

b)

DFG =k-1=2

DFE =N-k =93-3=90

DFT =92

Ho: all groups have the same mean rating

Ha: at least one group has a different mean rating

numerator df =2

denominator df =90

c)

DFG =k-1=2

DFE =N-k =45-3=42

DFT =44

Ho: all groups have the same quiz score

Ha: at least one group has a different mean quiz score

numerator df =2

denominator df =42

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