For each of the following situations, give the degrees of freedom for the group

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 20 of his hens to each of the three treatments. DFG = DFE = DFT = 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 99 responses, of which 30 were from students who attend varsity football or basketball games only, 18 were from students who also attend other varsity competitions, and 51 who did not attend any varsity games. DFG = DFE = DFT = 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 = numerator df denominator df

Explanation / Answer

a)

DFG = 2

DFE = 57 DFT = 59

H0: All groups have the same mean cholesterol level

Ha)- At least one group has a different mean cholesterol level.

b)

DFG = 2           .

DFE = 96   

DFT = 98

Ho   All groups have the same mean rating

Ha At least one group has a different mean rating

c)

DFG = 2

. DFE = 42

DFT =44

Ho  All groups have the same mean quiz score.

Ha   At least one group has a different mean quiz score

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