Sampling Distribution and Confidence Intervals

Sampling Distribution of Sample Proportions

• The sampling distribution of sample proportions is the distribution of sample proportions from all possible samples of a given size.

Large Sample Confidence Interval for a Proportion

• The large sample confidence interval for a proportion is used when the sample size is large enough to assume that the sampling distribution of sample proportions is approximately normal.
• The formula for the confidence interval is: p ± z*√(p(1-p)/n)
• where:
  • p is the sample proportion
  • z* is the critical value from the standard normal distribution
  • n is the sample size
• The margin of error is the amount added and subtracted from the sample proportion to create the confidence interval.

Plus Four Method: Adjustment to CI

• The plus four method is used when the sample size is small or when the sample proportion is close to 0 or 1.
• The plus four method adds two successes and two failures to the sample size and the number of successes.
• This helps to ensure that the confidence interval is more accurate.

Example: Large Sample CI for a Proportion

• An example of a large sample CI for a proportion is given in the text.
• This example demonstrates how to calculate the confidence interval for a proportion when the sample size is large enough to assume that the sampling distribution of sample proportions is approximately normal.

Example: Plus Four Method CI

• An example of a plus four method CI is given in the text.
• This example demonstrates how to calculate the confidence interval for a proportion when the sample size is small or when the sample proportion is close to 0 or 1.

Conditions Summary

• The conditions for using the large sample confidence interval for a proportion are:
  • The sample size is large enough to assume that the sampling distribution of sample proportions is approximately normal.
  • The sample is a random sample.
  • The population size is at least 10 times the sample size.
• The conditions for using the plus four method are:
  • The sample size is small.
  • The sample proportion is close to 0 or 1.

This quiz covers the concept of sampling distribution of sample proportions, how to calculate large sample confidence intervals, and the application of the plus four method for making adjustments to confidence intervals. Test your understanding of these statistical methods and their formulas.