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Unformatted text preview: Chapter 9: Comparing Two Means Readings: Chapter 9 April 20, 2010 1 Twoindependent Sample t Procedures • We are often interested in comparing two populations (or groups) based on a continuous measurement. – Compare postmortem serotonin levels in patients who died of heart disease (cases) vs. those who died from other causes (controls). – To evaluate impact of light on the growth of plants, one group of seedlings grows in dark conditions, and a second group gets the standard amount of light. Compare heights of plants after a specified time period. • Each group has different individuals who may receive different treatments. • Responses from each sample are independent of each other. • Goal: compare the population means of the two groups. • Notations: Population Mean Standard Deviation 1 μ 1 σ 1 2 μ 2 σ 2 Sample Sample size Mean Standard Deviation 1 n 1 ¯ x 1 s 1 2 n 2 ¯ x 2 s 2 Twosample t Confidence Intervals • The level C Confidence interval for μ 1 μ 2 is: ¯ x 1 ¯ x 2 ± t α 2 · s s 2 1 n 1 + s 2 2 n 2 , where t α 2 is the value for the t ( k ) density curve with area C between t α 2 and t α 2 . The value of the degrees of freedom k is approximated by software or we use k = min( n 1 1 ,n 2 1). Twosample t Test 1. Write the hypotheses in terms of the difference between means. H : μ 1 = μ 2 H a : μ 1 > μ 2 or H : μ 1 = μ 2 H a : μ 1 < μ 2 or H : μ 1 = μ 2 H a : μ 1 6 = μ 2 1 2. Calculate the test statistic t = ¯ x 1 ¯ x 2 q s 2 1 n 1 + s 2 2 n 2 3. Calculate the pvalue – For H a : μ 1 < μ 2 , pvalue = P ( T < t ), – For H a : μ 1 > μ 2 , pvalue = P ( T > t ), – For H a : μ 1 6 = μ 2 , pvalue = 2 P ( T >  t  ). where T ∼ t ( k ). The value of the degrees of freedom k is approximated using software or we use k = min( n 1 1 ,n 2 1)....
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This note was uploaded on 03/30/2011 for the course STAT 511 taught by Professor Bud during the Spring '08 term at Purdue.
 Spring '08
 BUD

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