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 12-41.
(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.

(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?

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Diet Type Patient Age Group 20-30 30-40 40-50 50-60 60-70 40 70 35 40 50 9 50 20 30 50