Question

A random sample of five observations from three normally distributed populations produced the following data: (You may find it useful to reference the F table.) Treatments A B C 31 29 23 29 25 20 22 28 21 31 15 16 31 17 23 x−A = 28.8 x−B = 22.8 x−C = 20.6 s2A = 15.2 s2B = 41.2 s2C = 8.3 Click here for the Excel Data File a. Calculate the grand mean. (Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.) b. Calculate SSTR and MSTR. (Round intermediate calculations to at least 4 decimal places and final answers to 4 decimal places.) c. Calculate SSE and MSE. (Round intermediate calculations to at least 4 decimal places and final answers to 4 decimal places.) d. Specify the competing hypotheses in order to determine whether some differences exist between the population means. H0: μA = μB = μC; HA: Not all population means are equal. H0: μA ≤ μB ≤ μC; HA: Not all population means are equal. H0: μA ≥ μB ≥ μC; HA: Not all population means are equal. e-1. Calculate the value of the F(df1, df2) test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

Answer 1

from above

a)

Grand average Xgrand =∑xi/N =

361/10=

24.0667

b)

SSTR =180.1333

MSTR =90.0667

c)

SSE =258.8000

MSE =21.5667

d)

H0: μA = μB = μC; HA: Not all population means are equal

e-1)

test statistic =4.176