A medical officer in a psychiatry department of a hospital wants to compare the family history of psychiatric disorder of patients, with and without depression

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A medical officer in a psychiatry department of a hospital wants to compare the family

history of psychiatric disorder of patients, with and without depression. The characteristics

of a random sample of 27 patients with depression were compared with the characteristics

of a random sample of 50 patients without depression. The study found that 12 of the

patients with depression has a family history of psychiatric disorder, while 18 of those

patients without depression has a family history of psychiatric disorder.

(i) Construct a 99% confidence interval for the difference in the population

percentages of patients with a family history of psychiatric disorder, with and

without depression.

(6 Marks)

(ii) Based on your confidence interval in (i), can we conclude that the population

percentages of patients with a family history of psychiatric disorder is not the same

for with and without major depression at 1% significance level?

(4 Marks)

(iii) How large the sample size would be if we wish to be at least 98% confident that

the error in estimating percentage of patients with no family history of psychiatric

disorder with depression is 4%?

(4 Marks)

(iv) Suppose that, three confidence intervals for the percentage of patients with a family

history of psychiatric disorder without depression are computed from the same

sample at 5% significance level. The intervals are ?22.70, 49.30?% ,

?24.83,100?% and ?0,47.17?%. For each confidence interval, explain why each

confident interval is different?