For each of the following situations, give the degrees of freedom for the group
ID: 3222252 • 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 15 of his hens to each of the three treatments.
H0:
All groups have the same mean cholesterol level.All groups have different mean cholesterol levels. The all-vegetarian diet group has a higher mean cholesterol level.The all-vegetarian diet group has a lower mean cholesterol level.At least one group has a different mean cholesterol level.
Ha:
At least one group has a different mean cholesterol level.All groups have the same mean cholesterol level. All groups have different mean cholesterol levels.The all-vegetarian diet group has a lower mean cholesterol level.The all-vegetarian diet group has a higher 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 92 responses, of which 31 were from students who attend varsity football or basketball games only, 18 were from students who also attend other varsity competitions, and 43 who did not attend any varsity games.
H0:
The group of students who do not attend games has a higher mean rating.All groups have different mean ratings. All groups have the same mean rating.The group of students who do not attend games has a lower mean rating.At least one group has a different mean rating.
Ha:
The group of students who do not attend games has a lower mean rating.All groups have different mean ratings. All groups have the same mean rating.At least one group has a different mean rating.The group of students who do not attend games has a higher mean rating.
(c) A professor wants to evaluate the effectiveness of his teaching assistants. In one class period, the 45 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 higher mean quiz score.At least one group has a different mean quiz score. All groups have the same mean quiz score.The group taught by the oldest TA has a lower mean quiz score.All groups have different mean quiz scores.
Ha:
At least one group has a different mean quiz score.All groups have different mean quiz scores. The group taught by the oldest TA has a lower mean quiz score.All groups have the same mean quiz score.The group taught by the oldest TA has a higher mean quiz score.
DFG = DFE = DFT =Explanation / Answer
Degrees of freedom for the group (DFG) = Number of Groups -1
Error (DFE) = DFT-DFG
and for the total (DFT) = Number of observations -1
Numerator Degrees of freedom = DFG
Denominator Degrees of freedom =DFE
(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 15 of his hens to each of the three treatments.
Number of Groups = 3 Groups :
Groups : two different cholesterol-lowering drugs added to the hen's standard diet and a all-vegetarian diet =3
Number of observations = 45 (He assigns 15 of his hens to each of the three treatments i.e 15x3 =45)
Degrees of freedom for the group (DFG) = Number of Groups -1 = 3-1 =2
Degrees of freedom for Total (DFT) = Number of observations -1 = 45-1=44
Degrees of freedom for Error (DFE) = DFT-DFG = 44-2=42
Numerator Degrees of freedom = DFG =2
Denominator Degrees of freedom =DFE =42
H0: All groups have the same mean cholesterol level
Ha: At least one group has a different mean cholesterol level
numerator df 2
denominator df 42
(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 92 responses, of which 31 were from students who attend varsity football or basketball games only, 18 were from students who also attend other varsity competitions, and 43 who did not attend any varsity games.
Number of Groups : 3 Groups
Group1 :students who attend varsity football or basketball games only
Groups 2: students who also attend other varsity competitions
Group 3 : Did not attend any varsity games
Number of observations = 92 (received 92 responses)
Degrees of freedom for the group (DFG) = Number of Groups -1 = 3-1 =2
Degrees of freedom for Total (DFT) = Number of observations -1 = 92-1 =91
Degrees of freedom for Error (DFE) = DFT-DFG = 91-2=89
Numerator Degrees of freedom = DFG =2
Denominator Degrees of freedom =DFE =89
H0: All groups have the same mean rating.
Ha: At least one group has a different mean rating.
numerator df 2
denominator df 89
(c) A professor wants to evaluate the effectiveness of his teaching assistants. In one class period, the 45 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(divided into three equal-sized groups)
Number of observtions =45
Degrees of freedom for the group (DFG) = Number of Groups -1 = 3-1 =2
Degrees of freedom for Total (DFT) = Number of observations -1 = 45-1 =44
Degrees of freedom for Error (DFE) = DFT-DFG = 44-2=42
Numerator Degrees of freedom = DFG =2
Denominator Degrees of freedom =DFE =42
H0: All groups have the same mean quiz score.
Ha: At least one group has a different mean quiz score
numerator df 2
denominator df 42
DFG = 2 DFE = 42 DFT = 44Related Questions
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