Week 5

# Week 5 - STAT 218 Week #5 Chapter 7 Questions from previous...

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STAT 218 Week #5 Chapter 7 Questions from previous Class/HW? Announcement: We will cover chapters 7, 8, 9 for the next test. CHAPTER 7 - COMPARISON OF TWO INDEPENDENT SAMPLES Important Chapter Two Sample Comparisons Confidence Intervals Hypotheses Testing P-values Effect Size and Power Illustrative Examples Is one sunscreen (both SPF 15) really better than another? Do Honda civic and Ford Escort hybrids get different gas millage? Is the medicine the doctor prescribed any better than a placebo? Will brand x fertilizer product more fruit than brand y? Compare two types of weight training for development of muscle mass? Consider two independent populations (Student Population at Cal Poly vs. xxx) and respective samples from each Picture – relationship of population space to sample Notation – means, standard deviations, standard errors Pictorial presentations we have learned – Physical fitness of Cal Poly Students vs xxx o Box plots for two Independent Samples o Two samples have same mean o Two samples with different means o Normal Distribution Curves o Two samples have same mean o Two samples with different means Basic Premise for comparing two populations You must get a representative sample from each of the two populations Ideally randomization – both samples were selected randomly from their respective populations For this problem, assume the distributions are normally distributed o Unnecessary assumption if the sample size is large (Central Limit Theorem) 1

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There are two approaches for comparing two populations Confidence Intervals Hypothesis Testing CONFIDENCE INTERVALS The Confidence Interval for the difference in means of two populations We are trying to estimate the difference in population means (µ 1 - µ 2 ) Recall Confidence Interval = estimate +/- (t or z) x SE Estimate ……the best estimate of the difference of two population means is the difference in sample means SE = Square root of the sum of the individual variances divided by their respective sample sizes (or the square root of the sum of the SE’s squared) Degrees of Freedom (DF) = The book gives you a complicated formula. You may use either a) the book definition, or b) (n1 -1) + (n2 -1). I will use the latter for all examples. Realize that the true DF is between (n1 - 1 + n2 - 1) and the smaller of (n1-1) and (n2-1). Know that fact. t distribution value: use the DF from above and the same CI techniques we used before Example – Compute two sided 90% confidence bounds for the difference of two populations when the sampling resulted in: CALPOLY - Sample #1: n = 15, mean = 43, Std Dev=11.0 XXX - Sample #2: n= 14, mean = 35, Variance = 144.0 Step #1 – Determine type of problem you have o Two Independent sample confidence interval Step #2 - Satisfy the assumptions o Two independent samples? o
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## This note was uploaded on 05/07/2008 for the course STAT 218 taught by Professor Staff during the Spring '08 term at Cal Poly.

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Week 5 - STAT 218 Week #5 Chapter 7 Questions from previous...

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