ESSENTIAL STATISTICS 2 E William Navidi and Barry
ESSENTIAL STATISTICS 2 E William Navidi and Barry Monk ©Mc. Graw-Hill Education. All rights reserved. Authorized only for instructor use in the classroom. No reproduction or further distribution permitted without the prior written consent of Mc. Graw-Hill Education.
The Central Limit Theorem for Proportions Section 6. 3 ©Mc. Graw-Hill Education.
Objectives 1. Construct the sampling distribution for a sample proportion 2. Use the Central Limit Theorem to compute probabilities for sample proportions ©Mc. Graw-Hill Education.
Objective 1 Construct the sampling distribution for a sample proportion ©Mc. Graw-Hill Education.
Sample and Population Proportion • ©Mc. Graw-Hill Education.
• • ©Mc. Graw-Hill Education.
An Example of a Sampling Distribution • ©Mc. Graw-Hill Education.
An Example of a Sampling Distribution (Continued) • Next, we compare these values to the population proportion (0. 5) and the sample size (5). ©Mc. Graw-Hill Education.
Mean and Standard Deviation of a Sampling Distribution • ©Mc. Graw-Hill Education.
Example: Sampling Distribution • • ©Mc. Graw-Hill Education.
Probability Histogram for a Sampling Distribution • • ©Mc. Graw-Hill Education.
Central Limit Theorem for Proportions • ©Mc. Graw-Hill Education.
Example 1: The Central Limit Theorem • ©Mc. Graw-Hill Education.
Example 2: The Central Limit Theorem • ©Mc. Graw-Hill Education.
Objective 2 Use the Central Limit Theorem to compute probabilities for sample proportions ©Mc. Graw-Hill Education.
Example 1: Using the Central Limit Theorem According to a recent Harris poll, chocolate is the favorite ice cream flavor for 27% of Americans. If a sample of 100 Americans is taken, what is the probability that the sample proportion of those who prefer chocolate is greater than 0. 30? • ©Mc. Graw-Hill Education.
Example 2: Using the Central Limit Theorem In the 2012 U. S. presidential election, 51% of voters voted for Barack Obama. If a sample of 75 voters were polled, would it be unusual if less than 40% of them had voted for Barack Obama? • ©Mc. Graw-Hill Education.
You Should Know. . . • ©Mc. Graw-Hill Education.
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