Final answer:
The sampling distribution of the proportion, assuming the null hypothesis is true, is a normal distribution centered at the expected proportion. The observed proportion represents the proportion observed in the sample, and the standard error measures the variability in the sample proportion.
Step-by-step explanation:
The sampling distribution of the proportion, assuming the null hypothesis is true, is a normal distribution centered at the expected proportion. The observed proportion represents the proportion observed in the sample, and the standard error measures the variability in the sample proportion.
For example, let's say we are conducting a study to estimate the proportion of students in a school who eat breakfast. We collect a simple random sample of 100 students and find that 60 of them eat breakfast. The expected proportion is the value we would expect to see if the null hypothesis (e.g., 50% of students eat breakfast) is true. In this case, the expected proportion would be 0.5.
The observed proportion is the proportion we actually observe in the sample. In this case, the observed proportion would be 0.6 (60/100).
The standard error measures the variability in the sample proportion. It is calculated as the square root of (expected proportion * (1 - expected proportion) / sample size). In this case, the standard error would be calculated as the square root of (0.5 * (1 - 0.5) / 100) = 0.05.