Question

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6. [20 points) In a trial of 175 patients who received 10-mg doses of a drug daily, 49 reported headaches as a side effect. Use this information to complete parts (a) through (c) below. a. Obtain a point estimate for the population proportion of patients who received 10- mg doses of a drug daily and reported headache as a side effect. b. Construct a 95% confidence interval for the population proportion of patients who receive the drug and report headache as a side effect. c. Interpret the confidence interval.

Answer 1

Solution :- Given That:- Favourable case: X = Sample size : n= 49 175 a) Point estimate : P = x/n 49 / 175 Ô = 0.28 At 95% Confidence Level'z' is, a = 1 - 95% a = 1 - 0.95 a = 0.05 a/2 = 0.025 By using standard normal table, za/2 = 1.96 At 95% Confidence interval for Population Proportion is, b) + margin of error P(1-0) 0 + 2a/2 n sqrt(0.28 *(1-0.28)/175) 0.28 + (1.96 ) 0.28 (0.0665) (0.214, 0.347) At 95% Confidence Interval for Population Proportion is, (0.214, 0.347) C) Interpretation :- We are 95% Confident that interval from 0.214 to 0.347 actually does contain the true value of Proportion