Chapter 10: Inference for Two Populations

When conducting a hypothesis test that compares two independent population proportions, the following characteristics should be present:

1. The two independent samples are simple random samples that are independent.
2. The number of successes is at least five, and the number of failures is at least five, for each of the samples.
3. Growing literature states that the population must be at least ten or 20 times the size of the sample. This keeps each population from being over-sampled and causing incorrect results.

Comparing two proportions, like comparing two means, is common. If two estimated proportions are different, it may be due to a difference in the populations or it may be due to chance. A hypothesis test can help determine if a difference in the estimated proportions reflects a difference in the population proportions.

Like the case of differences in sample means, we construct a sampling distribution for differences in sample proportions:

𝑝‘𝐴=𝑋𝐴𝑛𝐴 and 𝑝‘𝐵=𝑋𝐵𝑛𝐵 are the sample proportions for the two sets of data in question 𝑋𝐴 and 𝑋𝐵.

The difference of two proportions follows an approximate normal distribution. Generally, the null hypothesis states that the two proportions are the same. That is, H₀: p_A = p_B. To conduct the test, we use a pooled proportion, p_c.