A pharmaceutical company tested the impact of four cholesterol-reducing medications (denoted A, B, C and D) on people at high risk of heart attack. For this clinical trial 20 volunteers with LDL (bad) cholesterol levels of 140 mg/dl were randomly assigned to one of the four medications. The subjects were instructed to take one tablet per day for a period of three months after which their LDL levels were again measured. Below are the amounts (in mg/dl) by which the LDL levels decreased after the three month trial. | Medication A | Medication B | Medication C | Medication D 30 31 32 31.5 29 32 31.5 35 33 29 29 30.5 29.75 27 33 31 30 30.5 31.75 31 (a) Write an appropriate statistical model (to represent the responses using an appro- priate equation) to describe the above data. Describe all symbols/notations used in the model. b) Estimate the (four) group means, overall mean, and error variance (²) from the data. (c) Do the data provide sufficient evidence to indicate that at least one of the medi- cations produces a mean reduction in LDL cholesterol that is different from any of the other medications? Test at the 5% level of significance (show all working and include appropriate hypothesis statements).

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Author:Amos Gilat
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A pharmaceutical company tested the impact of four cholesterol-reducing medications
(denoted A, B, C and D) on people at high risk of heart attack. For this clinical trial
20 volunteers with LDL (bad) cholesterol levels of 140 mg/dl were randomly assigned to
one of the four medications. The subjects were instructed to take one tablet per day
for a period of three months after which their LDL levels were again measured. Below
are the amounts (in mg/dl) by which the LDL levels decreased after the three month trial.
| Medication A | Medication B | Medication C Medication D
31
30
31
30
32
31.5
32
35
29
30.5
29.75
27
33
30.5
31.75
31
29
31.5
33
29
(a) Write an appropriate statistical model (to represent the responses using an appro-
priate equation) to describe the above data. Describe all symbols/notations used in
the model.
(b) Estimate the (four) group means, overall mean, and error variance (²) from the
data.
(c) Do the data provide sufficient evidence to indicate that at least one of the medi-
cations produces a mean reduction in LDL cholesterol that is different from any of
the other medications? Test at the 5% level of significance (show all working and
include appropriate hypothesis statements).
Transcribed Image Text:A pharmaceutical company tested the impact of four cholesterol-reducing medications (denoted A, B, C and D) on people at high risk of heart attack. For this clinical trial 20 volunteers with LDL (bad) cholesterol levels of 140 mg/dl were randomly assigned to one of the four medications. The subjects were instructed to take one tablet per day for a period of three months after which their LDL levels were again measured. Below are the amounts (in mg/dl) by which the LDL levels decreased after the three month trial. | Medication A | Medication B | Medication C Medication D 31 30 31 30 32 31.5 32 35 29 30.5 29.75 27 33 30.5 31.75 31 29 31.5 33 29 (a) Write an appropriate statistical model (to represent the responses using an appro- priate equation) to describe the above data. Describe all symbols/notations used in the model. (b) Estimate the (four) group means, overall mean, and error variance (²) from the data. (c) Do the data provide sufficient evidence to indicate that at least one of the medi- cations produces a mean reduction in LDL cholesterol that is different from any of the other medications? Test at the 5% level of significance (show all working and include appropriate hypothesis statements).
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