Question

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 q table.)

x¯1 = 169, n1 = 5; x¯2 = 179, n2 = 5; x¯3 = 172, n3 = 5; x¯4 = 162, n4 = 5; MSE = 55.8

a. Use Fisher’s LSD method to determine which population means differ at α = 0.05. (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 DifferencesConfidence IntervalCan we conclude that the population means differ?μ1 − μ2[,]μ1 − μ3[,]μ1 − μ4[,]μ2 − μ3[,]μ2 − μ4[,]μ3 − μ4[,]

b. Use Tukey’s HSD method to determine which population means differ at α = 0.05. (If the exact value for nT – c is 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 DifferencesConfidence IntervalCan we conclude that the population means differ?μ1 − μ2[,]μ1 − μ3[,]μ1 − μ4[,]μ2 − μ3[,]μ2 − μ4[,]μ3 − μ4[,]

Answer 1

Here we have 4 groups and total number of observations are 20. So degree of freedom is

df= 20-4 = 16

(a)

Critical value of t for and df = 16 is 2.1199. The Fisher's LSD Value is

So confidence intervals are:

For :

Since confidence interval contains zero so we cannot conclude that populaiton means differ.

For :

Since confidence interval contains zero so we cannot conclude that populaiton means differ.

For :

Since confidence interval contains zero so we cannot conclude that populaiton means differ.

For :

Since confidence interval contains zero so we cannot conclude that populaiton means differ.

For :

Since confidence interval does not contain zero so we can conclude that populaiton means differ.

For :

Since confidence interval contains zero so we cannot conclude that populaiton means differ.

(b)

Critical value for , df=16 and k=4 is

So Tukey's HSD will be

So confidence intervals are:

For :

Since confidence interval contains zero so we cannot conclude that populaiton means differ.

For :

Since confidence interval contains zero so we cannot conclude that populaiton means differ.

For :

Since confidence interval contains zero so we cannot conclude that populaiton means differ.

For :

Since confidence interval contains zero so we cannot conclude that populaiton means differ.

For :

Since confidence interval does not contain zero so we can conclude that populaiton means differ.

For :

Since confidence interval contains zero so we cannot conclude that populaiton means differ.