Refer to given Exercise. Consider the following three contrasts:
(1) difference between the sum of the reduction in blood sugar levels using diet types 1 and 3 from that using diet types 2 and 4;
(2) difference between the sum of the reduction in blood sugar level using diet types 1 and 2 from that using diet types 3 and 4;
(3) difference in the sum of the reduction in blood sugar level using diet types 2 and 3 from that using diet types 1 and 4.
(a) Find the sum of squares due to each of the contrasts and discuss their contribution to the treatment sum of squares.
(b) What null hypothesis is indicated by contrast 1? Test the hypothesis at a 5% level of significance.
(c) What type of hypothesis is indicated by contrast 2? Test the hypothesis at the 10% level of significance.
Exercise
A doctor is contemplating four types of diet to reduce the blood sugar levels of patients. Because of differences in the metabolism of patients, the doctor categorizes the patients into five age groups. From each age group, four patients are selected and randomly assigned to the diets. After two months on the diet, the reduction in patients' blood sugar levels is found. The results are shown in Table.
(a) Is there a difference in the diet types as evidenced by the mean reduction in blood sugar level? Test at the 5% level of significance.
|
Patient Age Group
|
Diet Type
|
|
1
|
2
|
3
|
4
|
|
20-30
|
40
|
70
|
35
|
40
|
|
30-40
|
60
|
80
|
65
|
60
|
|
40-50
|
65
|
60
|
60
|
50
|
|
50-60
|
30
|
50
|
40
|
20
|
|
60-70
|
45
|
55
|
50
|
30
|
(b) Find a 90% confidence interval for the mean reduction in blood sugar level for diet type 1.
(c) Find a 95% confidence interval for the difference in the mean reduction in blood sugar levels between diet types 2 and 4. Is there a difference between the two diet types?
(d) Which diet type would you prefer?