Question

CH13 Q4

The following statistics are calculated by sampling from four normal populations whose variances are equal: (You may find it useful to reference the t table and the g table.) r1 = 137, n1 = 4; Tz = 144, n2 = 4; = 136, n3 = 4; T4 = 124, n4 = 4; MSE = 57.4 a. Use Fishers LSD method to determine which population means differ at a- 0.01. (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.) Population Mean Differences Can we conclude that the population means differ? Confidence Interval 2-H3b. Use Tukeys HSD method to determine which population means differ at a-0.01.(If the exact value for m-cis not found in the table, then round down. 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.) Population Mean Differences Can we conclude that the population means differ? Confidence Interval

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Answer #1

Fishers LSD critical value=tα/2,df √(MSE(1/ni+1/nj))

confidence interval= mean difference±critical value

Sample Sample
Group Mean Size
1 137 4
2 144 4
3 136 4
4 124 4
Other Data
Level of significance 0.01
Numerator d.f. 4
Denominator d.f. 12
MSE 57.4
t-critical (tα/2)= 3.05454
confidence interval
population mean difference mean difference critical value lower limit upper limit result
µ1-µ2 -7 16.3639
-23.364
9.364
Means are not different
µ1-µ3 1 16.3639
-15.364
17.364
Means are not different
µ1-µ4 13 16.3639
-3.364
29.364
Means are not different
µ2-µ3 8 16.3639
-8.364
24.364
Means are not different
µ2-µ4 20 16.3639
3.636
36.364
Means are different
µ3-µ4 12 16.3639
-4.364
28.364
Means are not different

b)

critical value = q*√(MSE/2*[1/ni+1/nj])

confidence interval = mean difference ± critical value

if confidence interval contans zero, then means are not different.

Sample Sample
Group Mean Size
1 137 4
2 144 4
3 136 4
4 124 4
Level of significance 0.01
Numerator d.f. 4
Denominator d.f. 12
MSE 57.4
Q Statistic 5.5
confidence interval
population mean difference mean difference critical value lower limit upper limit result
µ1-µ2 -7 20.8348 -27.83 13.835 Means are not different
µ1-µ3 1 20.8348 -19.83 21.83 Means are not different
µ1-µ4 13 20.8348 -7.835 33.83 Means are not different
µ2-µ3 8 20.83476662 -12.83 28.83 Means are not different
µ2-µ4 20 20.83476662 -0.835 40.83 Means are not different
µ3-µ4 12 20.83476662 -8.835 32.83 Means are not different
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