## 15.5Chapter 15 Summary

Chapter Specifics

• A parameter in a statistical problem is a number that describes a population, such as the population proportion p. To estimate an unknown parameter, use a statistic calculated from a sample, such as the sample proportion .
• The law of large numbers for proportions states that the actual observed sample proportion must approach the population proportion p as the number of observations increases.
• The sampling distribution of a statistic describes the values of the statistic in all possible samples of the same size from the same population.
• When the sample is an SRS from the population, the mean of the sampling distribution of the sample proportion is the same as the population proportion p. That is, is an unbiased estimator of p.
• The standard deviation of the sampling distribution of is for an SRS of size n when the population proportion is p. The standard deviation of the sampling distribution gets smaller only at the rate .
• Choose an SRS of size n from a population with population proportion p. When n is large, the sampling distribution of is approximately Normal. We can use the distribution to calculate approximate probabilities for events involving , provided both np and n(1 − p) are 10 or more.

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