Answer :
Answer:
a) [tex]\hat{p} = 0.27[/tex]
b) All the conditions are met for constructing a confidence interval.
Step-by-step explanation:
We are given the following in the question:
Sample size, n = 167
Number of people who had side effects, x = 45
a) point estimate
[tex]\hat{p} = \dfrac{x}{n} = \dfrac{45}{167} = 0.27[/tex]
The point estimate for the population proportion of patients who received 10-mg doses of a drug daily and reported headache as a side effect is 0.27
b) Conditions for constructing a confidence interval
- The data is a random sample from the population of interest.
- Individual observations can be considered independent.
[tex]n\hat{p}>10\\167\times 0.27 = 45.09 > 10\\n(1-\hat{p})>10\\167(1-0.27) = 121.91 > 10[/tex]
Thus, all the conditions are met for constructing a confidence interval.