Question

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

a.

Point estimate for population proportion is the sample proportion.

Let p be the population proportion of people who recieved 10mg doses of drug and reported headache

Point estimate for population proportion, p̂ = x/n

where x is the number of people reported headache in the sample of n people who received the drug

Here, n = 175 and x = 49

Therefore, p̂ = 49/175

= 0.28

b.

The 95% confidence interval for population proportion of people who recieved 10mg doses of drug and reported headache is given by

p̂ ± Z* [ p̂*(1-p̂)/n ]^1/2

For 95% confidence interval , Z = 1.96

The confidence interval is given by:

0.28  ± 1.96 * [ 0.28 * (1-0.28) / 175 ]^1/2

= 0.28 ± 0.067

= [ 0.213, 0.347 ]

c.

The 95% confidence interval for the population proportion gives an interval of values that we can be 95% sure contains the population proportion.

So , we can be 95% certain that the population proportion lies between 0.213 and 0.347