For each of the following situations, give the degrees of freedom for the group
ID: 3172337 • 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.
H0:
At least one group has a different mean cholesterol level.
All groups have the same mean cholesterol level.
The all-vegetarian diet group has a higher mean cholesterol level.
All groups have different mean cholesterol levels.
The all-vegetarian diet group has a lower mean cholesterol level.
Ha:
The all-vegetarian diet group has a lower mean cholesterol level.
All groups have different mean cholesterol levels.
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.
(b) A researcher is interested in students' opinions regarding an additional annual fee to support non-income-producing varsity sports. Students were asked to rate their acceptance of this fee on a seven-point scale. She received 94 responses, of which 31 were from students who attend varsity football or basketball games only, 15were from students who also attend other varsity competitions, and 48 who did not attend any varsity games.
H0:
The group of students who do not attend games has a lower mean rating.The group of students who do not attend games has a higher mean rating. All groups have the same mean rating.At least one group has a different mean rating.All groups have different mean ratings.
Ha:
The group of students who do not attend games has a lower mean rating.
At least one group has a different mean rating.
All groups have different mean ratings.
The group of students who do not attend games has a higher mean rating.
All groups have the same mean rating.
(c) A professor wants to evaluate the effectiveness of his teaching assistants. In one class period, the 42 students were randomly divided into three equal-sized groups, and each group was taught power calculations from one of the assistants. At the beginning of the next class, each student took a quiz on power calculations, and these scores were compared.
H0:
The group taught by the oldest TA has a lower mean quiz score.
The group taught by the oldest TA has a higher mean quiz score.
At least one group has a different mean quiz score.
All groups have different mean quiz scores.
All groups have the same mean quiz score.
Ha:
At least one group has a different mean quiz score.
The group taught by the oldest TA has a lower mean quiz score.
The group taught by the oldest TA has a higher mean quiz score.
All groups have the same mean quiz score.
All groups have different mean quiz scores.
DFG = DFE = DFT =Explanation / Answer
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.
Number of Groups = 3 as two different chlesterol -lowering drugs and a all vegetarian diet are being compared
Total number of data points collected = 3 x 30 =90; As 30 hens assigned to each group
Degrees of freedom for the group (DFG) = Number of Groups -1 = 3-1=2
Degrees of freedom for the error (DFE) = DFT - DFG = 89-2 = 87
Degrees of freedom for thethe total (DFT) =Total number of data points -1 = 90-1=89
H0:
All groups have the same mean cholesterol level.
Ha:
At least one group has a different mean cholesterol level.
Numerator df = Degrees of freedom for the group (DFG) = Number of Groups -1 = 3-1=2
Denominator df = Degrees of freedom for the error (DFE) = DFT - DFG = 89-2 = 87
(b) A researcher is interested in students' opinions regarding an additional annual fee to support non-income-producing varsity sports. Students were asked to rate their acceptance of this fee on a seven-point scale. She received 94 responses, of which 31 were from students who attend varsity football or basketball games only, 15were from students who also attend other varsity competitions, and 48 who did not attend any varsity games.
Number of Groups = 3 as reponses received from three groups . Group1 : Students who attended football or basketball games only. Group 2: students who also attend varsity football or basketball games ; Group3 : Students who did not attend any varsity games.
Total number of data points collected = Total number of responses received : 94
Degrees of freedom for the group (DFG) = Number of Groups -1 = 3-1=2
Degrees of freedom for the error (DFE) = DFT - DFG = 93-2 = 91
Degrees of freedom for thethe total (DFT) =Total number of data points -1 = 94-1=93
H0:
All groups have the same mean rating.
Ha:
At least one group has a different mean rating.
Numerator df = Degrees of freedom for the group (DFG) = Number of Groups -1 = 3-1=2
Denominator df = Degrees of freedom for the error (DFE) = DFT - DFG = 93-2 = 91
(c) A professor wants to evaluate the effectiveness of his teaching assistants. In one class period, the 42 students were randomly divided into three equal-sized groups, and each group was taught power calculations from one of the assistants. At the beginning of the next class, each student took a quiz on power calculations, and these scores were compared.
Number of Groups = 3 ; 3 Equal-sized groups
Total number of data points collected = Total number of responses received : 42
Degrees of freedom for the group (DFG) = Number of Groups -1 = 3-1=2
Degrees of freedom for the error (DFE) = DFT - DFG = 41-2 = 39
Degrees of freedom for thethe total (DFT) =Total number of data points -1 = 42-1=41
H0:
All groups have the same mean quiz score.
Ha:
At least one group has a different mean quiz score.
Numerator df = Degrees of freedom for the group (DFG) = Number of Groups -1 = 3-1=2
Denominator df = Degrees of freedom for the error (DFE) = DFT - DFG = 41-2 = 39
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