proportions

Question 1

What is the formula for estimating the proportion of successes (p^ ) in a binomial experiment?

Answer 1

^p = x/n

where

x = number of successes,

n = total trials.

Question 2

What are the four conditions for a binomial distribution?

Answer 2

Only two outcomes per trial (success/failure).

Constant probability of success (
p
p).

Fixed number of trials (
n
n).

Independent trials.

Question 3

When should you use the Wilson interval instead of the normal approximation?

Answer 3

When:

Sample size (n) is small, or p^ is close to 0 or 1 (e.g., <0.05 or >0.95).

Question 4

What is the null hypothesis (H0) for a one-sample proportion z-test?

Answer 4

H0:p=p0

where p0 is the hypothesized population proportion.

Question 5

What does an odds ratio (OR) of 1 imply?

Answer 5

No difference between groups (e.g., treatment = control).

OR > 1: Higher odds in group 1.

OR < 1: Higher odds in group 2.

Question 6

Why is the log of the odds ratio used for confidence intervals?

Answer 6

The sampling distribution of
log(OR) is more symmetric/normal, especially for small samples. The SE is: sqrt 1/a + 1/b + 1/c + 1/d