Name: One factor ANOVA ANOVA table Source Mean n Std. Dev 55.806 77.20 6 51.50 6

Question

Name: One factor ANOVA ANOVA table Source Mean n Std. Dev 55.806 77.20 6 51.50 6 61.50 18 SS df MS value 2.477 Bottom 3.103 Middle Treatment 1.648 Top 2,273.880 2 1,136.9400 184.57 2.74E-11 Error 92.400 156.1600 11.798 Total Total 2,366.280 17 Find Individual confidence intervals for following three pairwise differences. Then compare the width of each interval with the Tukey simultaneous confidence intervals we found last time (look at slide 21) Individual confidence intervals: [ -ih ±ta/2 MSE (1 + 1) ni nh Individual confidence interval for 44-lg: Individual confidence interval for Individual confidence interval for HT HB:

Explanation / Answer

The 95% c.i for muM-muB=(xbarM-xbarB)+-(qalpha/sqrt 2)*sqrt MSE*sqrt(1/nM+1/nB), where, xbar is sample mean, qlapha for k=3, v=n-k=18-3=15 is 3.67, n is sample size, k is number of treatments.

=(77.20-55.80)+-3.67*sqrt 6.16*sqrt(1/6+1/6)

=21.4+-5.2589

=16.1411, 26.6589

Equivalently, 95% c.i for muM-muT=(77.20-51.50)+-5.2589=20.4411, 30.9589

95% c.i for muT-muB=(51.50-55.80)+-5.2589=(-9.5589,-2.0411)

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