lab7f09_ans

# lab7f09_ans - Stat 401C Prob#1 Lab#7 Key Fall 2009 (a)...

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Stat 401C Lab#7 Key Fall 2009 Prob#1 (a) Hartley’s test requires that (1) the sample sizes are equal, and (2) that they are random samples from normal distributions. The first condition is obviously met. Except for one data value for Die 2 (which may be an outlier), the box plots indicate symmetric distributions and the normal probability plots do not show deviations from linearity, that might indicate that these sample are not drawn from normal distributions. We choose to ignore that one point and assume normality for each population. (b) Test 2 3 2 2 2 1 0 : σ = = H vs. : a H at least one pair unequal From the above 34348 . 0 , 21917 . 4 , 98174 . 1 2 3 2 2 2 1 = = = s s s . Thus the Hartley’s test statistic is: 28 . 12 34348 . 0 21917 . 4 max = = F and R.R. is 25 . 3 max > F (from Table 12, at 05 . = α , with t=3 and df2=17, and using interpolation to approximate between df2=15 and 20). Thus reject 0 H at 05 . = (c) Tests that the Variances are Equal Test F Ratio DFNum DFDen Prob > F O'Brien[.5] 4.3582 2 51 0.0179* Brown-Forsythe 7.4938 2 51 0.0014* Levene 8.0194 2 51 0.0009* Bartlett 10.6442 2 . <.0001* Levene’s test: Since the p-value .0009 is clearly less than .05 we reject 0 H that the variances are equal.

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x y x^2 y^2 xy 21 175.79 441 30902.1241 3691.59 24 221.47 576 49048.9609 5315.28 32 281.03 1024 78977.8609 8992.96 47 407.84 2209 166333.4656 19168.48 50 454.68 2500 206733.9024 22734 59 548.03 3481 300336.8809 32333.77 68 594.55 4624 353489.7025 40429.4 74 658.06 5476 433042.9636 48696.44 62 542.03 3844 293796.5209
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## lab7f09_ans - Stat 401C Prob#1 Lab#7 Key Fall 2009 (a)...

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