Question 3

A medical social researcher wishes to investigate the proportion of Type II diabetic patients in a given country town who take insulin to manage their diabetes. Therefore, they surveyed a random sample of 121 Type II diabetes patients across the medical practices in the city, and 42 reported taking insulin to manage their diabetes.

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a) What is the proportion of Type II diabetics in the town that take insulin?

b) Check this data for the necessary conditions for each type of confidence interval on a proportion.

c) Calculate a 95% confidence interval for the proportion of Type II diabetic patients using insulin in this

town.

A nationally accepted level of insulin use from long-term data is 42%.

d) Based on the above confidence interval, explain if there is evidence that the Type II diabetes patients in this

town have a different rate of use of insulin to the rest of the nation.

e) Perform a test of significance at a significance level of 0.05 if there is evidence that the Type II diabetes

patients in this town have a different rate of use of insulin to the rest of the nation.

f) If the researcher wanted to halve the margin of error in the confidence interval found, what sample size

would be required for the same data and level of confidence? No Full calculation is required for this answer.