For each of the following situations, give the degrees of freedom for the group
ID: 3222052 • 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 45 of his hens to each of the three treatments.
H0:
All groups have the same mean cholesterol level.
The all-vegetarian diet group has a lower mean cholesterol level.
At least one group has a different mean cholesterol level.
All groups have different mean cholesterol levels.
The all-vegetarian diet group has a higher mean cholesterol level.
Ha:
The all-vegetarian diet group has a higher mean cholesterol level.
All groups have the same mean cholesterol level.
At least one group has a different mean cholesterol level.
The all-vegetarian diet group has a lower mean cholesterol level.
All groups have different mean cholesterol levels.
DFG = DFE = DFT =Explanation / Answer
Solution : Correct Hypotheses would be-
H0: All groups have the same mean cholesterol level.
Ha: At least one group has a different mean cholesterol level.
For computing degrees of freedom, we follow-
(1) If there are n total data points collected, then there are n1 total degrees of freedom.
(2) If there are m groups being compared, then there are m1 degrees of freedom associated with the factor of interest.
F-statistic follows an F-distribution with m1 numerator degrees of freedom and nm denominator degrees of freedom. Therefore, we'll calculate the P-value, as it appears in the column labeled P, by comparing the F-statistic to an F-distribution with m1 numerator degrees of freedom and nm denominator degrees of freedom.
Considering above we can numerator df here will be 3-1 = 2 and
denominator df will be 45 - 3 = 42
ANSWER
TY!
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