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Chapter 10 Lecture Outline

# Chapter 10 Lecture Outline - CHAPTER 10 Estimating...

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CHAPTER 10 Estimating Proportions with Confidence Review of Ch 9 information we will use in Ch 10: One Proportion – one categorical variable If np and n(1-p) are both greater than or equal to 10, then the distribution of p ˆ ’s can be described as: the shape is approximately normal the mean is p the standard deviation is n p p ) 1 ( - the standard error is n p p ) ˆ 1 ( ˆ - Two Proportions – two categorical variables If n 1 p 1 ,n 1 (1-p 1 ), n 2 p 2 and n 2 (1-p 2 ) are all greater than or equal to 10, then the distribution of 2 1 ˆ ˆ p p - ’s can be described as: the shape is approximately normal the mean is p 1 -p 2

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the standard deviation is 2 2 2 1 1 1 ) 1 ( ) 1 ( n p p n p p - + - the standard error is 2 2 2 1 1 1 ) ˆ 1 ( ˆ ) ˆ 1 ( ˆ n p p n p p - + - Multiplier values: We can use the z- table in reverse (similar to percentiles) to get common z* multipliers for CI’s about proportions. CI level: Look for this probability: z*: 80 90 95 98 99 As the sample size increases the standard error will decrease and the confidence interval gets smaller. So a larger sample size gives us a more precise estimate of our parameter. As the confidence level increases, the multiplier increases leading to a wider confidence interval. Confidence intervals have the general form: Sample estimate ± Margin of error OR Sample estimate ± Multiplier * Standard Error
Interpretation: We are _____% confident that the true (population parameter) of <variable> is between _____ and _____. For two proportions, indicate which proportion is higher or lower

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Chapter 10 Lecture Outline - CHAPTER 10 Estimating...

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