Question

Chapter 13 Analysis of Variance Saved Help Save & Exl Chec 3 The following statistics are computed by sampling from three normal populations whose variances are equal: (You may find it useful to reference the ttable and the gtable.) 10 points a. Calculate 99% confidence intervals for μ1-μ2, μ1 -μ3, and μ2-μ3 to test for mean differences with Fisher's LSD approach. (Negative values should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places. Round your answers to 2 decimal places.) oBook Population Mean Differences Can we conclude that the population means differ? Confidence Interval Print References b. Repeat the analysis with Tukey's HSD approach. (If the exact value for nT-cis not found in the table, then round down. Negative values should be indicated by』minus sign. Round intermediate calculations to at least 4 decimal places. Round your answers to 2 decimal places.) Population Mean Differences Can we conclude that the population means differ? Confidence Interval

Answer 1

Here we have 3 groups and total number of observations are 8+10+5=23. So degree of freedom is

df= 23-3 = 20

(a)

Critical value of t for and df = 20 is 2.845. The Fisher's LSD Value is

α 0.01

$LSD=t_{\alpha/2}\sqrt{MSE\left (\frac{1}{n_{1}}+\frac{1}{n_{2}} \right )}=2.845\cdot \sqrt{33.4\cdot \left (\frac{1}{n_{i}}+\frac{1}{n_{j}} \right )}$

The required confidence interval is

xbari-xbarj absolute diff 7.5 7.5 7.1 xbarj 39.3 39.3 46.4 Upper limit Significant(Yes/No) 0 No No groups (i-j) mu1-mu2 mu1-mu3 mu2-mu3 xbari 31.8 31.8 39.3 Lower limit 15.3 15.3 16.11 ni nj 10 7.7991 10 7.7991 7.5 7.5 7.1 0.3 0.3 1.91 8 10 9.0057

(b)

Critical value for , df=20 and k=3 is

α 0.01

$q=4.64$

So Tukey's HSD will be

$HSD=q\sqrt{\frac{MSE}{2}\left ( \frac{1}{n_{i}}+\frac{1}{n_{j}} \right )}=4.64\sqrt{\frac{33.4}{2}\left ( \frac{1}{n_{i}}+\frac{1}{n_{j}} \right )}$

The required confidence intervals are:

groups (i-j) mu1-mu2 mu1-mu3 mu2-mu3 Significant(Yes/No) No No No xbari 31.8 31.8 39.3 xbarj 39.3 39.3 46.4 HSD 8.994 8.994 10.386 xbari-xbarj Lower limit Upper lmit 1.49 1.49 3.29 ni 8 8 10 nj 10 10 16.49 16.49 17.49 7.1