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Lect19_L6_L7_handout

# Lect19_L6_L7_handout - lecture 19 Condence Intervals III...

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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

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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 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 business-majored collage graduates who have a starting salary more than 15000? we will discuss soon

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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? re-assign value 0 if the number is not negative, 1 if the number is negative, new list: 0, 1, 0, 0, 0, 1.
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Lect19_L6_L7_handout - lecture 19 Condence Intervals III...

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