Answer:
We need a sample of at least 2090 families if we want to be 95% confident that our estimate of p is within 0.02 of the true value.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of , and a confidence interval , we have the following confidence interval of proportions.
In which
z is the zscore that has a pvalue of .
The margin of error of the interval is:
In this problem, we have that:
95% confidence interval
So , z is the value of Z that has a pvalue of , so .
How large a sample is required if we want to be 95% confident that our estimate of p is within 0.02 of the true value?
The margin of error decreases when the sample size increases. So we need a sample of at least n people when M = 0.02 for the estimate of p being within 0.02 of the value.
So
We need a sample of at least 2090 families if we want to be 95% confident that our estimate of p is within 0.02 of the true value.