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Chapter9_print - Chapter 9: Comparing Two Means Readings:...

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Unformatted text preview: Chapter 9: Comparing Two Means Readings: Chapter 9 April 20, 2010 1 Two-independent 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 1 1 2 2 2 Sample Sample size Mean Standard Deviation 1 n 1 x 1 s 1 2 n 2 x 2 s 2 Two-sample t Confidence Intervals The level C Confidence interval for 1- 2 is: x 1- x 2 t 2 s s 2 1 n 1 + s 2 2 n 2 , where t 2 is the value for the t ( k ) density curve with area C between- t 2 and t 2 . The value of the degrees of freedom k is approximated by software or we use k = min( n 1- 1 ,n 2- 1). Two-sample t Test 1. Write the hypotheses in terms of the difference between means. H : 1 = 2 H a : 1 > 2 or H : 1 = 2 H a : 1 < 2 or H : 1 = 2 H a : 1 6 = 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 p-value For H a : 1 < 2 , p-value = P ( T < t ), For H a : 1 > 2 , p-value = P ( T > t ), For H a : 1 6 = 2 , p-value = 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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Chapter9_print - Chapter 9: Comparing Two Means Readings:...

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