Chapter 8 Estimation Understanding Basic Statistics Fifth Edition By Brase and Brase Prepared by Jon Booze

8 | 2 Copyright © Cengage Learning. All rights reserved. Estimating p in the Binomial Distribution We will use large-sample methods in which the sample size, n, is fixed. We assume the normal curve is a good approximation to the binomial distribution if both np > 5 and nq = n(1 – p) > 5.

8 | 3 Copyright © Cengage Learning. All rights reserved. Point Estimates in the Binomial Case

8 | 4 Copyright © Cengage Learning. All rights reserved. Margin of Error The magnitude of the difference between the actual value of p and its estimate is the margin of error.

8 | 5 Copyright © Cengage Learning. All rights reserved. The Distribution of For large samples, the distribution is well approximated by a normal distribution.

8 | 6 Copyright © Cengage Learning. All rights reserved. A Probability Statement With confidence level c, as before.

8 | 7 Copyright © Cengage Learning. All rights reserved.

8 | 8 Copyright © Cengage Learning. All rights reserved. Public Opinion Polls

8 | 9 Copyright © Cengage Learning. All rights reserved. Choosing Sample Sizes When designing statistical studies, it is good practice to decide in advance: –The confidence level –The maximal margin of error Then, we can calculate the required minimum sample size to meet these goals.

8 | 10 Copyright © Cengage Learning. All rights reserved. Sample Size for Estimating μ If σ is unknown, use σ from a previous study or conduct a pilot study to obtain s. Always round n up to the next integer!!

8 | 11 Copyright © Cengage Learning. All rights reserved. Sample Size for Estimating If we have no preliminary estimate for p, use the following modification:

8 | 12 Copyright © Cengage Learning. All rights reserved. Sample Size for Estimating How many students should be surveyed to determine the proportion of students who prefer vanilla ice cream to chocolate, accurate to 0.1 at a 90% confidence level? a). 100b). 69c). 52d). 5

8 | 13 Copyright © Cengage Learning. All rights reserved. Sample Size for Estimating How many students should be surveyed to determine the proportion of students who prefer vanilla ice cream to chocolate, accurate to 0.1 at a 90% confidence level? a). 100b). 69c). 52d). 5