© 2001 Prentice-Hall, Inc.Chap 8-1 BA 201 Lecture 12 Confidence Interval Estimation

© 2001 Prentice-Hall, Inc. Chap 8-2 Topics Properties of as an Estimate for Confidence Interval Estimation for the Mean ( Known)

© 2001 Prentice-Hall, Inc. Chap 8-3 Unbiased Property of ( ) BiasedUnbiased p.253

© 2001 Prentice-Hall, Inc. Chap 8-4 Effect of Large Sample (Consistency ) Larger sample size Smaller sample size p.253 For Sampling with Replacement: As n increases, decreases

© 2001 Prentice-Hall, Inc. Chap 8-5 Less Variability (Efficiency) Sampling Distribution of Median Sampling Distribution of Mean p.253 Standard Error (Standard Deviation) of the Sampling Distribution is Less than the Standard Error of Other Unbiased Estimators

© 2001 Prentice-Hall, Inc. Chap 8-6 Confidence Interval Estimates Mean  Unknown Confidence Intervals Proportion  Known

© 2001 Prentice-Hall, Inc. Chap 8-7 Confidence Interval for ( Known) Assumptions Population standard deviation is known Population is normally distributed If population is not normal, use large sample Confidence Interval Estimate is called the sampling error or margin of error

© 2001 Prentice-Hall, Inc. Chap 8-8 Obtaining Confidence Interval in PHStat PHStat | Confidence Interval | Estimates for the Mean, sigma known

© 2001 Prentice-Hall, Inc. Chap 8-9 Example A random sample of 15 stocks traded on the NASDAQ market showed an average shares traded to be From past experience, it is believed that the population standard deviation of shares traded is and the shares traded are very closed to a normal distribution. Construct a 99% confidence interval for the average shares traded on the NASDAQ market. Interpret your result. PHStat output The 99% CI for the population mean:

© 2001 Prentice-Hall, Inc. Chap Sampling Distribution of the Mean Interval and Level of Confidence Confidence Intervals Intervals extend from to of the intervals constructed contain ; do not. _

© 2001 Prentice-Hall, Inc. Chap 8-11 Example: Interpretation (continued) We are 99% confidence that the population average number of shares traded on NASDAQ is between and If all possible samples of size 15 are taken and the corresponding 99% confidence intervals are constructed, 99% of the confidence intervals that are constructed will contain the true unknown population mean. For this particular confidence interval [85309, ], the unknown population mean can either be in the interval or not in the interval. It is, therefore, incorrect to state that the probability is 99% that the unknown population mean will be in the interval [85309, ].

© 2001 Prentice-Hall, Inc. Chap 8-12 Example: Interpretation (continued) Using the confidence interval method on repeated sampling, the probability that we will have constructed a confidence interval that will have contain the unknown population mean is 99%.

© 2001 Prentice-Hall, Inc. Chap 8-13 Summary Addressed Properties of as an Estimate for Discussed Confidence Interval Estimation for the Mean ( Known)