Question

A researcher asks random samples of residents of two separate counties as to whether they had purchased organically grown food in the last three months. He wants to determine whether the proportion of residents of one county who purchase organically grown food is greater than the proportion of residents of the second county who purchase organically grown food. Choose the appropriate test and name the population(s).

Answer 1

2 proportions z test

The two populations are named as residents from the first county and residents from the second county.

Explanation:

This is testing hypothesis about the difference between two proportions.

When the proportions are tested if they are the test statistic

z= ( p^1-p^2)- (p1-p2) / √p₁q₁/n₁ + p₂q₂/ n₂

where p^1 is the proportion of success in the first sample and p^2 of size n₁ is the proportion of success in the second sample of size n₂ with unknown proportions of successes p1 and p2 respectively.

When the sample sizes are sufficiently large

z= ( p^1-p^2)- (p1-p2) / √p₁q₁/n₁ + p₂q₂/ n₂ is approximately standard normal.

The two populations are named as residents from the first county and residents from the second county.