# 48 4152 s 1101 1715 17 26 two sample t signicance test

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Unformatted text preview: tributions 16 / 26 Two-sample t signiﬁcance test example A special class is designed to improve reading abilities. Compare a control group with a treatment group −→ two independent samples Treatment group 24 61 59 46 43 44 52 43 58 67 62 57 71 49 54 43 53 57 49 56 33 Control 42 33 43 41 55 19 26 54 62 20 37 85 K310 Statistical Techniques group 46 37 10 42 17 55 60 28 53 48 42 Group Treatment Control n 21 23 Inference for Distributions x ¯ 51.48 41.52 s 11.01 17.15 17 / 26 Two-sample t signiﬁcance test example Group Treatment Control 1 n 21 23 x ¯ 51.48 41.52 s 11.01 17.15 Hypotheses: K310 Statistical Techniques Inference for Distributions 18 / 26 Two-sample t signiﬁcance test example Group Treatment Control n 21 23 x ¯ 51.48 41.52 s 11.01 17.15 H0 : µ1 = µ2 Ha : µ1 > µ2 1 Hypotheses: 2 Test statistic: 3 P -value: 4 Conclusion, α = 0.02: K310 Statistical Techniques Inference for Distributions 18 / 26 Two-sample t conﬁdence interval Suppose we have random sample of size n1 from normal population #1 random sample of size n2 from normal population #2 2 2 and we don’t know the means µ1 , µ2 , and the variances σ1 , σ2 are not generally the same. The conﬁdence interval for µ1 − µ2 is (¯1 − x2 ) ± t ∗ x ¯ 2 s2 s1 +2 n1 n2 where t ∗ is from the t (k ) distribution where k = min(n1 − 1, n2 − 1) (or approximated by software) K310 Statistical Techniques Inference for Distributions 19 / 26 Two-sample t conﬁdence interval example What is the 95% conﬁdence interval for the mean improvement by the students in the previous example? (¯1 − x2 ) ± t ∗ x ¯ 2 s1 s2 +2 n1 n2 = (51.48 − 41.52) ± t ∗ 11.011 17.152 + 21 23 = 9.96 ± 4.31t ∗ K310 Statistical Techniques Inference for Distributions 20 / 26 Two-sample t conﬁdence interval example What is the 95% conﬁdence interval for the mean improvement by the students in the previous example? (¯1 − x2 ) ± t ∗ x ¯ 2 s1 s2 +2 n1 n2 = (51.48 − 41.52) ± t ∗ 11.011 17.152 + 21 23 = 9.9...
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## This note was uploaded on 04/16/2013 for the course MATH-M 310 taught by Professor Palanivelmanoharan during the Spring '13 term at Indiana.

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