Question

Random sampling from four normally distributed populations produced the following data: (You may find it useful to reference the F table.)

Treatments

A

B

C

D

−12

−20

−5

−20

−20

−9

−18

−20

−11

−13

−17

−20

−19

−7

−16

Click here for the Excel Data File

a. Calculate the grand mean. (Negative value should be indicated by a minus sign. Round your answer to 2 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.

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

• p-value < 0.01

f. At the 10% 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 α = 0.10.

• 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

applying one way ANOVA

Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	105.1167	3	35.03889	1.383362	0.299223	3.587434
Within Groups	278.6167	11	25.32879
Total	383.7333	14

a) grand mean =-15.13

b)SSTR =105.1167

and MSTR =35.0389

c)

SSE =278.6167

MSE =25.3288

d)

H₀: μ_A = μ_B = μ_C; H_A: Not all population means are equal

e-1 )F =1.383

e-2)

p-value > 0.10

f)

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

g)

We cannot conclude that some means differ.