Lecture 22- CI Two Proportions

Question 1

An epidemiologist wants to estimate the proportion of women with
asthma. Find the sample size (n) needed to give an estimate for this
proportion with a margin of error no more than 0.03 with 95% confidence.

Answer 1

1067.11 < n
So we need at least 1067.11 people. We round up to the next whole
person, so the minimum n = 1068

Working on lecture slides

Question 2

When rearranging what do you have to be careful of in terms of inequalities?

Answer 2

Divide or times by a negative number= flip the inequality

Question 3

When you ‘flip’ the confidence interval and are trying to find the number of people that will give you a certain margin of error what P value do you use and why?

Answer 3

Use p= 0.5 cause this will give the the maximum value for p(1-p)= 0.25

It’s better to be more conservative and work out out a number of people that gives a margin of error more precise than necessary then to underestimate. We have to assume P so we only have one variable and can solve for n

Question 4

How do you view risk difference in terms of proportions (think contingency tables)?

Answer 4

minus one sample proportion of the other

Is just the difference between two proportions

Question 5

If the sample size is big enough what will the sampling distribution for the difference in proportions be like? What does this mean?

Answer 5

-Will reasonable a normal distribution (central limit theorem)
-Therefore, can use this knowledge of the sampling distribution to
construct a confidence interval for the true difference in proportions.

Question 6

Work through problem on slide 422

Question 7

What is the margin of error for a proportion given by?

Answer 7

multiplier x standard error

multiplier is always 1.96 as using normal, not t, for proportions
standard error is the square root of p(1-p)/n