Statistics Chapter 8: Sample Proportion

Comparison of Sections 8.1 and 8.2

• Section 8.1 centered on the distribution of the sample mean.
• Section 8.2 shifts focus to the distribution of the sample proportion (p-hat).
• Sample proportion is vital for estimating the prevalence of a specific characteristic in a population.

Sample Proportion (p-hat)

• Symbolized as p-hat, it represents the estimated proportion of individuals who possess a certain characteristic within a defined population.

Sampling Distribution of p-hat

• The sampling distribution illustrates the variety of sample proportions that can occur in different samples drawn from the same population.
• This distribution allows for assessment of how p-hat varies from sample to sample.

Standard Deviation of the Sampling Distribution

• A crucial measure for determining how much p-hat is expected to fluctuate across different samples.
• It helps evaluate the precision of p-hat as an estimate of the population proportion.

Z-Score of p-hat

• Calculated by taking the difference between the sample proportion and the population proportion, then dividing by the standard deviation of the population.
• Useful for assessing how far the sample proportion is from the expected population proportion in standard deviation units.