Final answer:
The appropriate distribution for testing a hypothesis about a population proportion is the standard normal distribution. The sample proportion is found by dividing the number of successes in the sample by the number sampled. The conditions np > 5 and nq > 5 must be met for the binomial distribution of a sample proportion to be approximated by a normal distribution.
Step-by-step explanation:
When testing a hypothesis about a population proportion, the appropriate distribution to use is the standard normal distribution.
To find the sample proportion, you divide the number of successes in the sample by the total number sampled.
The standard normal distribution is used because the binomial distribution of a sample proportion can be approximated by a normal distribution when the conditions np > 5 and nq > 5 are met.
The mean of the normal distribution is equal to the population proportion, and the standard deviation is sqrt((p*q)/n), where p is the population proportion and q = 1 - p.
For example, if you wanted to test a hypothesis about the proportion of students who like pizza in a school, you would take a sample of students, count the number of students who like pizza, and divide that by the total sample size to find the sample proportion.
Then, using the standard normal distribution, you can calculate the z-score and determine the p-value to evaluate the hypothesis.