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 35 of his hens to each of the three treatments.
Answer:
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DFG |
= |
|
|
DFE |
= |
|
|
DFT |
= |
H0:
(a)At least one group has a different mean cholesterol level.
(b)All groups have the same mean cholesterol level.
(c)All groups have different mean cholesterol levels.
(d)The all-vegetarian diet group has a lower mean cholesterol level.
(e)The all-vegetarian diet group has a higher mean cholesterol level.
Ha:
(a)All groups have the same mean cholesterol level.
(b)At least one group has a different mean cholesterol level.
(c)The all-vegetarian diet group has a higher mean cholesterol level.
(d)The all-vegetarian diet group has a lower mean cholesterol level.
(e)All groups have different mean cholesterol levels.
Answer:
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numerator df= |
|
|
denominator df= |
(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 97 responses, of which 30 were
from students who attend varsity football or basketball games only,
15were from students who also attend other varsity competitions,
and 52 who did not attend any varsity games.
Answer:
|
DFG |
= |
|
|
DFE |
= |
|
|
DFT |
= |
H0:
(a)The group of students who do not attend games has a higher mean rating.
(b)All groups have the same mean rating.
(c)The group of students who do not attend games has a lower mean rating.
(d)At least one group has a different mean rating.
(e)All groups have different mean ratings.
Ha:
(a)The group of students who do not attend games has a lower mean rating.
(b)All groups have the same mean rating.
(c)The group of students who do not attend games has a higher mean rating.
(d)All groups have different mean ratings.
(e)At least one group has a different mean rating.
Answer:
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numerator df= |
|
|
denominator df= |
(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.
Answer:
|
DFG |
= |
|
|
DFE |
= |
|
|
DFT |
= |
H0:
(a)All groups have the same mean quiz score.
(b)The group taught by the oldest TA has a higher mean quiz score.
(c)At least one group has a different mean quiz score.
(d)All groups have different mean quiz scores.
(e)The group taught by the oldest TA has a lower mean quiz score.
Ha:
(a)The group taught by the oldest TA has a higher mean quiz score.
(b)All groups have different mean quiz scores.
(c)All groups have the same mean quiz score.
(d)The group taught by the oldest TA has a lower mean quiz score.
(e)At least one group has a different mean quiz score.
Answer:
|
numerator df= |
|
|
denominator df= |
a)
DFG = k-1= 1
DFE = N-k = 35-2 = 33
DFT = N-1 = 34
Null Hypothesis H0: All groups have the same mean cholesterol level.
Alternative Hypothesis H1: At least one group has a different mean cholesterol level.
Numerator DF = 1
Denominator DF = 33
b) DFG = k-1= 3-1= 2
DFE = N-k = 97-3 = 94
DFT = N-1 = 97-1 = 96
Null Hypothesis H0: All groups have the same mean rating.
Alternative Hypothesis H1: At least one group has a different mean rating
Numerator Df = 2
Denominator DF = 94
c)
DFG = k-1= 3-1= 2
DFE = N-k = 45-3= 42
DFT = N-1= 44
Null Hypothesis H0: All groups have the same mean quiz score.
Alternative Hypothesis H1: At least one group has a different mean quiz score.
Numerator df = 2
Denominator Df = 42
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