A random sample of five observations from three normally distributed populations

ID: 3071596 • Letter: A

Question

A random sample of five observations from three normally distributed populations produced the following data: Use Table 4.

Treatments

Calculate the grand mean. (Round your answer to 2 decimal places.)

Calculate SSTR and MSTR. (Round your final answers to 2 decimal places.)

Calculate SSE and MSE. (Round your final answers to 2 decimal places.)

Specify the competing hypotheses in order to determine whether some differences exist between the population means.

Calculate the value of the F(df1,df2) test statistic. (Round your final answer to 2 decimal places.)

Using the critical value approach at the 1% significance level, what is the conclusion to the test?

A random sample of five observations from three normally distributed populations produced the following data: Use Table 4.

The statistical software output for this problem is:

Analysis of Variance results:
Data stored in separate columns.

Column statistics

ANOVA table

Hence,

a) Grand mean = 23.73

b) SSTR = 34.53

MSTR = 17.27

c) SSE = 276.4

MSE = 23.03

d) H0: A = B = C; HA: Not all population means are equal. Option A is correct.

e) Test statistic = 0.75

f) Option D is correct.

Column n Mean Std. Dev. Std. Error A 5 24.6 3.9749214 1.7776389 B 5 21.6 3.5777088 1.6 C 5 25 6.363961 2.8460499

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