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
19	31	25
31	30	30
27	27	22
20	32	21
17	28	31
xA = 22.8	xB = 29.6	xC = 25.8
s2A2 = 35.2	s2B2 = 4.3	s2C2 = 20.7

Click here for the Excel Data File

a. Calculate the grand mean. (Round final answer to 4 decimal places.)

b. Calculate SSTR and MSTR. (Round final answers to 4 decimal places.)

c. Calculate SSE and MSE. (Round final answers to 4 decimal places.)

d. Specify the competing hypotheses in order to determine whether some differences exist between the population means. multiple choice 1

H₀: _A = _B = _C; H_A: Not all population means are equal.

H₀: _{A B C}; H_A: Not all population means are equal.

H₀: _{A B C}; H_A: Not all population means are equal.

e-1. Calculate the value of the F_{(df1, df2)} test statistic. (Round final answer to 3 decimal places.)

e-2. Find the p-value. multiple choice 2

0.05 p-value < 0.10

0.025 p-value < 0.05

0.01 p-value < 0.025

p-value < 0.01

p-value 0.10

f. At the 10% significance level, what is the conclusion to the test? multiple choice 3

Reject H₀ since the p-value is less than significance level.

Do not reject H₀ since the p-value is not less than significance level.

Do not reject H₀ since the p-value is less than significance level.

Reject H₀ since the p-value is not less than significance level.

g. Interpret the results at = 0.10. multiple choice 4

We cannot conclude that some means differ.

We conclude that some means differ.

We conclude that all means differ.

We conclude that population mean C is greater than population mean A.