The following statistics are computed by sampling from threenormal populations whose variances are equal: (You may findit useful to reference the t table andthe q table.)
xbar = 26.5, n1 = 7; xbar−2= 32.2,n2 = 8; xbar 3= 35.7, n3 =6; MSE = 33.2
a. Calculate 99% confidence intervals forμ1 − μ2,μ1 − μ3, andμ2 − μ3 to test for meandifferences with Fisher’s LSD approach. (Negative valuesshould be indicated by a minus sign. Round intermediatecalculations to at least 4 decimal places. Roundyour answers to 2 decimal places.)
| Population Mean Difference | Confidence Interval | Can we conclude that the population meansdiffer? |
|---|
| mu 1 -mu 2 | | |
| mu 1- mu 3 | | |
| mu 2 - mu 3 | |
b. Repeat the analysis with Tukey’s HSDapproach. (If the exact value for nT –c is not found in the table, then round down. Negativevalues should be indicated by a minus sign. Round intermediatecalculations to at least 4 decimal places. Round your answers to 2decimal places.)
| Population Mean Difference | Confidence Interval | Can we conclude that the population meansdiffer? |
|---|
| mu 1 -mu 2 | | |
| mu 1- mu 3 | | |
| mu 2 - mu 3 | |
c. Which of these two approaches would you useto determine whether differences exist between the populationmeans?
Tukey's HSD Method since it protects against an inflated risk ofType I Error.
Fisher's LSD Method since it protects against an inflated riskof Type I Error.
Tukey's HSD Method since it ensures that the means are notcorrelated.
Fisher's LSD Method since it ensures that the means are notcorrelated.
