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Chapter 11 Lecture Outline

# Chapter 11 Lecture Outline - CHAPTER 11 Estimating Means...

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CHAPTER 11 Estimating Means with Confidence Review of Ch 9 information we will use in Ch 10: One Mean – one quantitative variable If the population is normal or n≥30 then the x ’s can be described as: the shape is approximately normal the mean is μ the standard deviation is n σ the standard error is n s Mean of Paired Differences – two dependent quantitative variables If the population of differences is normal or n≥30 then the d ’s can be described as: the shape is approximately normal the mean is μ d the standard deviation is n d σ

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the standard error is n s d Two Independent Means – one quantitative variable and one categorical variable with two independent groups If both populations are normal or have n≥30 then the 2 1 x x - ’s can be described as: the shape is approximately normal the mean is μ 1 - μ 2 the standard deviation is 2 2 2 1 2 1 n n σ σ + the standard error is 2 2 2 1 2 1 n s n s + Confidence intervals have the general form: Sample estimate ± Margin of error OR Sample estimate ± Multiplier * Standard Error Multiplier values: When dealing with quantitative data, we use a t-multiplier (as opposed to the z-multiplier we used with a proportion). Why?
The shape of quantitative data is not always normal, but as the sample size increases, the distribution of the sample mean (x-bar) becomes more bell-shaped. Because of this, when computing a CI for quantitative data, we need a multiplier that reflects sample size (n). In the t-distribution, sample size is reflected in the degrees of freedom: df=n-1. So t* is a better multiplier for a CI for means than z* would be. How do we determine the t* multiplier ? The table is located before the z-table in the back cover of the textbook; labeled t* Multipliers for CIs and Rejection Region Critical Values, also table A.2 in the text, page 728. To use the t* multiplier table we need to know the confidence level and the sample size. For example, suppose we want a 95% C.I. for the population mean using a sample of size n=13. Our degrees of freedom would be df = n-1 = 13 – 1 = 12. So, to find the multiplier we would look across the df = 12 row and down the .95 confidence level column. We find that our t* multiplier is 2.18.

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