10_25_2 - t test and pooled variance. Use a 5% level of...

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STAT 420 Examples for 10/25/2007 Fall 2007 1. The country of Neverland has a range of mountains that stretches all the way across the country from North to South. We wish to test whether the average height of adult males born in the Western half of the country is different from the average height of adult males born in the Eastern half. We obtain a random sample of 6 adult male Neverlandians who were born in the Western half of the country, and a random sample of 8 adult males who were born in the Eastern half. The heights of the 14 individuals in inches are as follows: West: 65, 68, 67, 66, 71, 68. East: 68, 70, 67, 71, 70, 72, 73, 69. Assume that the populations are approximately normally distributed, and that the overall variances are equal. a) Compute 1 y , 2 y , 2 1 s , and 2 2 s . b) Test for difference in the average heights for these two groups using the
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Unformatted text preview: t test and pooled variance. Use a 5% level of significance. What can you say about the p-value of this test? ( ) ( ) 2 1 1 2 1 2 2 2 2 1 1 2 pooled-+-+-= n n s n s n s To test H : 1 2 = Assumptions: 1) Both populations are normal. 2) The population standard deviations are equal. Test Statistic: t = ( ) 2 1 pooled 2 1 1 1 & n n s y y +-- . n 1 + n 2 2 degrees of freedom The t Distribution r t 0.40 t 0.25 t 0.10 t 0.05 t 0.025 t 0.01 t 0.005 12 0.259 0.695 1.356 1.782 2.179 2.681 3.055 c) Test for difference in the average heights for these two groups using the ANOVA F test. Use a 5% level of significance. What can you say about the p-value of this test? ANOVA table: Source SS DF MS F Between Within Total The F Distribution v 1 v 2 1 = 0.10 12 3.18 = 0.05 4.75 = 0.01 9.33...
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This note was uploaded on 04/29/2010 for the course STAT stat 420 taught by Professor Stepanov during the Spring '07 term at University of Illinois at Urbana–Champaign.

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10_25_2 - t test and pooled variance. Use a 5% level of...

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