Verizon 4:44 PM For each of the following situations, give the degrees of freedo
ID: 3350212 • Letter: V
Question
Verizon 4:44 PM For each of the following situations, give the degrees of freedom for the group (OFG), for error (OFE), and for the total (DFT). State the null and alternative hypotheses, Ho 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 40 of his hens to each of the three treatments DFG DFE Mo: O The all-vegetarian diet group has a lower mean cholesterol level. O At least one group has a different mean cholesterol level. All groups have the same mean cholesterol level. OAll groups have different mean cholesterol levels. O The all-vegetarian diet group has a higher mean cholesterol level, Ha: O The all-vegetarian diet group has a lower mean cholesterol level. O All groups have the same mean cholesterol level. O The all-vegetarian diet group has a higher mean cholesterol level. O At least one group has a different mean cholesterol level. O All groups have different mean cholesterol levels. numerator d 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 93 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 44 who did not attend any varsity games DFE Mo: O At least one group has a different mean rating. All groups have the same mean rating, All groups have different mean ratings O The group of students who do not attend games has a lower mean rating. O The group of students who do not attend games has a higher mean rating. Ha: O At least one group has a different mean rating. O The group of students who do not attend games has a lower mean rating. OAll groups have different mean ratings. O The group of students who do not attend games has a higher mean rating.Explanation / Answer
Part (a)
Number of treatments = 3 => DFG = 3 – 1 = 2 ANSWER 1
Total number of observations (number of hens) = 120 => DFT = 120 – 1 = 119 ANSWER 3
The above two => DFE = DFT – DFG = 119 – 2 = 117 ANSWER 2
Since question talks of only comparing and not grading, the alternative would be ‘not all means are equal’ or ‘at least one mean is different’ and null hypothesis would always be ‘no change’ or ‘all means are equal. Thus,
H0: option 3, i.e., All groups have the same mean cholesterol level. ANSWER 4
HA: option 4, i.e., At least one group has a different mean cholesterol level. ANSWER 5
For F-statistic, the numerator degrees of freedom is always the DFG and the denominator degrees of freedom is always the DFE. Thus,
Numerator degrees of freedom = 2 ANSWER 6
Denominator degrees of freedom = 117 ANSWER 7
Part (b)
Number of students groups under study = 3 => DFG = 3 – 1 = 2 ANSWER 1
Total number of observations (number of students) = 93 => DFT = 93 – 1 = 92 ANSWER 3
The above two => DFE = DFT – DFG = 92 – 2 = 90 ANSWER 2
Since question talks of only comparing and not grading, the alternative would be ‘not all means are equal’ or ‘at least one mean is different’ and null hypothesis would always be ‘no change’ or ‘all means are equal. Thus,
H0: option 2, i.e., All groups have the same mean rating. ANSWER 4
HA: option 1, i.e., At least one group has a different mean rating. ANSWER 5
For F-statistic, the numerator degrees of freedom is always the DFG and the denominator degrees of freedom is always the DFE. Thus,
Numerator degrees of freedom = 2 ANSWER 6
Denominator degrees of freedom = 90 ANSWER 7
Part (c)
Number of students groups under study = 3 => DFG = 3 – 1 = 2 ANSWER 1
Total number of observations (number of students) = 42 => DFT = 42 – 1 = 41 ANSWER 3
The above two => DFE = DFT – DFG = 41 – 2 = 39 ANSWER 2
Since question talks of only comparing and not grading, the alternative would be ‘not all means are equal’ or ‘at least one mean is different’ and null hypothesis would always be ‘no change’ or ‘all means are equal. Thus,
H0: option 3, i.e., All groups have the same mean quiz score. ANSWER 4
HA: option 5, i.e., At least one group has a different mean quiz score. ANSWER 5
For F-statistic, the numerator degrees of freedom is always the DFG and the denominator degrees of freedom is always the DFE. Thus,
Numerator degrees of freedom = 2 ANSWER 6
Denominator degrees of freedom = 39 ANSWER 7
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