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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