# Two Sample t test for Comparing Two Means.docx - Two Sample...

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Two Sample t test for Comparing Two Means Requirements : Two normally distributed but independent populations, σ is unknown Hypothesis test Formula : where and are the means of the two samples, Δ is the hypothesized difference between the population means (0 if testing for equal means), s 1 and s 2 are the standard deviations of the two samples, and n 1 and n 2 are the sizes of the two samples. The number of degrees of freedom for the problem is the smaller of n 1 – 1 and n 2 – 1. An experiment is conducted to determine whether intensive tutoring (covering a great deal of material in a fixed amount of time) is more effective than paced tutoring (covering less material in the same amount of time). Two randomly chosen groups are tutored separately and then administered proficiency tests. Use a significance level of α < 0.05. Let μ 1 represent the population mean for the intensive tutoring group and μ 2 represent the population mean for the paced tutoring group. null hypothesis : H 0 : μ 1 = μ 2 or H 0 : μ 1 – μ 2 = 0 alternative hypothesis : H a : μ 1 > μ 2 or: H a : μ 1 – μ 2 > 0
The degrees of freedom parameter is the smaller of (12 – 1) and (10 – 1), or 9. Because this is a