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
	23				24				29
	16				17				31
	31				17				27
	17				27				16
	28				30				16
x−Ax−A	=	23.0		x−Bx−B	=	23.0		x−Cx−C	=	23.8
s2AsA2	=	43.5		s2BsB2	=	34.5		s2CsC2	=	52.7

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: μ_A = μ_B = μ_C; H_A: Not all population means are equal.

• H₀: μ_A ≤ μ_B ≤ μ_C; H_A: Not all population means are equal.

• H₀: μ_A ≥ μ_B ≥ μ_C; H_A: 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.)

e-2. Find the p-value.

• p-value  0.10
• 0.05  p-value < 0.10
• 0.025  p-value < 0.05
• 0.01  p-value < 0.025

• p-value < 0.01

f. At the 1% significance level, what is the conclusion to the test?

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

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

• 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.

g. Interpret the results at αα = 0.01.

• We conclude that some means differ.

• We cannot conclude that some means differ.

• We cannot conclude that all means differ.

• We cannot conclude that population mean C is greater than population mean A.

Answer 1