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
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