Duke University : Hypothesis Test for a Single Proportion

INSTRUCTIONS

1. Set the hypothesis

• H0 : p = null value
• H1 : p < or > or != null value

2. Check conditions

• Independence: Sampled observations must be independent (random sample/assignment & if sampling without replacement, n < 10% of population)
• Sample size/skew: np >= 10 and n(1-p) >= 10

3. Calculate the point estimate p̂
4. Draw sampling distribution, calculate test statistic, shade p-value,
   
5. Make a decision, and interpret it in context of the research question:

• If p-value < alpha, reject H0; the data provide convincing evidence for H1
• If p-value > alpha, fail to reject H0 the data do not provide convincing evidence for H1

When to use p̂ vs p?

• Use the sample proportion p̂ for confidence interval when when you don’t know the population proportion.
• Use the population proportion p or at least the null hypothesized value of the population proportion when we’re doing a hypothesis test which dictates that we must assume that the null hypothesis is true

(example)