STAT 462 - HW 3 Solution Key

STAT 462 - HW 3 Solution Key - Stat 462 Spring 2008...

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Stat 462, Spring 2008Homework 3 Solution key  Due February 15, 2008 Prepared by: Esra Kurum 2.3 (10 points) The student’s statement is incorrect. The p-value is high (0.91>0.05) so we fail to reject the null  hypothesis (  As a result, since we conclude that there is no linear association between X and  Y, we can’t make a comment about the slope. 2.4 (15 points-6 points for each a and b, 3 points for c) Regression Analysis: Y versus X (for question 1.19) The regression equation is Y = 2.11 + 0.0388 X Predictor Coef SE Coef T P Constant 2.1140 0.3209 6.59 0.000 X 0.03883 0.01277 3.04 0.003 S = 0.623125 R-Sq = 7.3% R-Sq(adj) = 6.5% Analysis of Variance Source DF SS MS F P Regression 1 3.5878 3.5878 9.24 0.003 Residual Error 118 45.8176 0.3883 Total 119 49.4055 a) As given in the minitab result above,   and from t-table  The 99% Confidence interval (CI) for   is: Then Since zero is not in the interval, we will reject the null hypothesis   and conclude that there is a linear  association between X and Y. The reason that the director of admissions are interested in 
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Stat 462, Spring 2008Homework 3 Solution key  Due February 15, 2008 Prepared by: Esra Kurum whether the interval includes zero is to test the null hypothesis that there is no linear association  between X and Y. b) Decision rule is if      then reject null hypothesis, where  Since   we reject the null hypothesis and conclude that   and there is a linear  association between ACT score(X) and GPA(Y). c) In the minitab  result given below the p-value is 0.003, since it is less than 0.01 we reject the null  hypothesis as we did in part a and part b.
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