Calculating Confidence Intervals for Means and Proportions in Statistics, Slides of Statistics

Download Calculating Confidence Intervals for Means and Proportions in Statistics and more Slides Statistics in PDF only on Docsity! Estimation docsity.com Point Estimation 1. Using a sample statistic to estimate a population parameter docsity.com Example of Interval Estimation 1. Dr. Violet wants to determine the average number of arrests that police officers make 2. She selects a sample of 58 police officers, and calculates M = 2.3 and SEM = 1.1 3. She can be 68% confident that µ lies somewhere in the interval of 1.2 to 3.4 docsity.com Properties of Good Estimators 1. Unbiased 1. Mean of sampling distribution is equal to the parameter being estimated docsity.com Confidence Intervals and the Normal Distribution 1. 95%: 1.96 2. 99%: 2.58 docsity.com Confidence Intervals and the Mean for Small Samples 1. N  30 2. M  t * SEM docsity.com Example of Small Sample Confidence Interval 1. Dr. Daisy wants to know the average number of grades that juvenile delinquents fail 2. She selects a sample of 28, and finds M = 1.4 and SEM = 0.3 3. She wants to be 99% confident 4. 1.4 ± 2.771(0.3) 5. She can be 99% confident that µ lies somewhere in the interval of 0.5687 to 2.2313 docsity.com t-Distribution 1. Infinite number of curves, based on number of degrees of freedom docsity.com Confidence Intervals and Proportions for Large Samples 1. N > 30 2. p  z * SEP docsity.com Standard Error of the Proportion n pp P )1(   docsity.com Estimating the Standard Error of the Proportion 1. Conservative approach 1. Set p = .5 docsity.com Example of Small Sample Confidence Interval for a Proportion • Dr. Felicia wants to determine what proportion of the general population is in favor of decriminalizing marijuana • She selects a sample 26, and finds p = .34 and SEP = 0.5 • She wants to be 95% confident • .34 ± 2.06(0.5) • She can be 95% confident that P lies somewhere in the interval of 0.327 to 0.353 docsity.com Using the SPSS Explore Procedure to Generate Confidence Intervals • Analyze, Descriptive Statistics, Explore • Move Dependent Variable over to Dependent List • Move Independent Variable over to Factor List • Statistics button – Set confidence level under Confidence Interval for Mean • Default value is 95% docsity.com