CHAPTER 7 Sampling Distributions 7 2 Sample Proportions

CHAPTER 7 Sampling Distributions 7. 2 Sample Proportions The Practice of Statistics, 5 th Edition Starnes, Tabor, Yates, Moore Bedford Freeman Worth Publishers

Sample Proportions Learning Objectives After this section, you should be able to: ü FIND the mean and standard deviation of the sampling distribution of a sample proportion. CHECK the 10% condition before calculating the standard deviation of the sample proportions. ü DETERMINE if the sampling distribution of sample proportions is approximately Normal. ü If appropriate, use a Normal distribution to CALCULATE probabilities involving a sample proportion. The Practice of Statistics, 5 th Edition 2

The Sampling Distribution of Consider the approximate sampling distributions generated by a simulation in which SRSs of Reese’s Pieces are drawn from a population whose proportion of orange candies is either 0. 45 or 0. 15. What do you notice about the shape, center, and spread of each? The Practice of Statistics, 5 th Edition 3

The Sampling Distribution of What did you notice about the shape, center, and spread of each sampling distribution? The Practice of Statistics, 5 th Edition 4

The Sampling Distribution of In Chapter 6, we learned that the mean and standard deviation of a binomial random variable X are As sample size increases, the spread decreases. The Practice of Statistics, 5 th Edition 5

The Sampling Distribution of a Sample Proportion As n increases, the sampling distribution becomes approximately Normal. Before you perform Normal calculations, check that the Normal condition is satisfied: np ≥ 10 and n(1 – p) ≥ 10. The Practice of Statistics, 5 th Edition 6

The Sampling Distribution of The Practice of Statistics, 5 th Edition 7

Sample Proportions Section Summary In this section, we learned how to… ü FIND the mean and standard deviation of the sampling distribution of a sample proportion. CHECK the 10% condition before calculating the standard deviation of the sample proportions. ü DETERMINE if the sampling distribution of sample proportions is approximately Normal. ü If appropriate, use a Normal distribution to CALCULATE probabilities involving a sample proportion. The Practice of Statistics, 5 th Edition 8