For each of the following situations, give the degrees of freedom for the group (DFG), for…

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.

DFG
=

DFE
=

DFT
=

H0:
The all-vegetarian diet group has a lower 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 higher mean
cholesterol level.At least one group has a different mean
cholesterol level.

Ha:
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.At least one group has a different
mean cholesterol level.All groups have the same mean cholesterol
level.

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 98 responses, of which 31 were
from students who attend varsity football or basketball games only,
16 were from students who also attend other varsity competitions,
and 51 who did not attend any varsity games.

DFG
=

DFE
=

DFT
=

H0:
At least one group has a different 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 higher mean rating.The group of students who do not attend games
has a lower mean rating.

Ha:
The group of students who do not attend games has a higher mean
rating.All groups have different mean
ratings.    At least one group has a different
mean rating.All groups have the same mean rating.The group of
students who do not attend games has a lower mean rating.

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.

DFG
=

DFE
=

DFT
=

H0:
The group taught by the oldest TA has a lower mean quiz
score.All groups have different mean quiz
scores.    All groups have the same 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.

Ha:
At least one group has a different mean quiz score.All groups
have the same mean quiz score.    All groups
have different mean quiz scores.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.

numerator df

denominator
df

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