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Unformatted text preview: lecture 19, Confidence Intervals III and Hypothesis Testing I Review Confidence Intervals for a Population Proportion Null and Alternative Hypotheses and Errors in Hypothesis Testing lecture 19, Confidence Intervals III and Hypothesis Testing I Outline 1 Review 2 Confidence Intervals for a Population Proportion 3 Null and Alternative Hypotheses and Errors in Hypothesis Testing lecture 19, Confidence Intervals III and Hypothesis Testing I Review Confidence Intervals for a Population Proportion Null and Alternative Hypotheses and Errors in Hypothesis Testing lecture 19, Confidence Intervals III and Hypothesis Testing I Review Review • General formula for confidence interval: • Point Estimate ± (Critical Value)(Standard Error) • Sampling distribution for sample proportion: If a random sample of size n is taken from a population then the sampling distribution of the sample proportion is (notation: population proportion =: p ; sample proportion =: ˆ p ) • Approximately normal, if n large ( np ≥ 10 and n ( 1 p ) ≥ 10) • Has a mean that equals p • Has standard deviation σ ˆ p ≈ q p ( 1 p ) n (exactly equal if the population size N is infinity, approximately equal when N is much larger than n ( N / n ≥ 20)) lecture 19, Confidence Intervals III and Hypothesis Testing I Review Confidence Intervals for a Population Proportion Null and Alternative Hypotheses and Errors in Hypothesis Testing lecture 19, Confidence Intervals III and Hypothesis Testing I Confidence Intervals for a Population Proportion Motivating Example, Starting Salaries • Interested in starting salary of HK college graduates who majored in business. • A sample of 100 is taken, the data look like the following: (HKD per month) 9800, 20700, 13200, 11800, 10050, ... • How do you construct a 95% confidence interval for the mean salary? • calculate the sample average, use it as a point estimate of the population mean • estimate the SE (using the sample standard deviation divided by √ n ). • figure out the critical value based on t distribution (or normal distribution because they are quite similar when n large) • How do you construct a 95% confidence interval for the proportion of HK businessmajored collage graduates who have a starting salary more than 15000? • we will discuss soon lecture 19, Confidence Intervals III and Hypothesis Testing I Review Confidence Intervals for a Population Proportion Null and Alternative Hypotheses and Errors in Hypothesis Testing lecture 19, Confidence Intervals III and Hypothesis Testing I Confidence Intervals for a Population Proportion Connection Between Mean and Proportion ( 2nd visit ) • A toy example: • a list of numbers 2, 3, 1, 8, 1, 5 • what is the proportion of negative numbers on the list?...
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This note was uploaded on 12/30/2009 for the course ISOM ISOM111 taught by Professor Anthonychan during the Fall '09 term at HKUST.
 Fall '09
 AnthonyChan

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