STATS 250 1st Edition Lecture 7 Outline of Last Lecture I. Parameters, Statistics, and Statistical InferenceII. From curiosity to Questions about ParametersIII. SD Module 0: an Overview of Sampling DistributionsIV. SD Module 1: Sampling Distributions for One Sample ProportionOutline of Current Lecture I. CI Module 0: an Overview of Confidence IntervalsII. CI Module 1: Confidence Interval for a Population Proportion pCurrent LectureI. CI Module 0: an Overview of Confidence Intervalsa. Sample estimate: provides our best guess as to what is the value of the population parameters, but it is not 100% accuratei. Value of the sample estimate varies from one sample to the nextii. Standard error of the sample estimate: provides an idea of how far away it would tend to vary from the parameter value on averageb. General format for a confidence interval estimate: sample estimate +/- standard errorsi. How many standard errors added or subtracted depends on confidence levelii. Confidence level: reflects how confident we are in the procedure, or the percentage of the time we expect the procedure to produce an interval that does contain the population parameter1. Commonly denoted n percentageII. CI Module 1: Confidence Interval for a Population Proportion pa. Sampling Distribution of pp i. If the sample size n is large and np ≥ 10 and n(1-p) ≥ 10ii. Then is approximately N(p, pp√p(1−p)n)iii. About 95% of the possible sample proportion values will be in the intervalp± 2√p(1−p)n1. Thus, about 95% of the intervals pp± 2√p(1−p)n will contain the population proportion b. Therefore, a 95% confidence interval for the true proportion p is given by: pp± 2√p(1−p)ni. However, because we don’t know the value p, we replace the value of p in the standard deviation with the value ppii. This creates Standard Error: √pp(1− pp)niii. And so the approximate 95% confidence interval for the population proportion p is given by: pp± 2√pp(1−