Treatments -20 -7 -19 -18 -8 -4 -17 -7 -18 -12 -19 -15 -13 -19 -13

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

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

Grand mean =

b. Calculate SSTR and MSTR. (Round intermediate calculations to at least 4 decimal places and final answers to 4 decimal places.)

SSTR = 

MSTR = 

c. Calculate SSE and MSE. (Round intermediate calculations to at least 4 decimal places and final answers to 4 decimal places.)

SSE = 

MSE =

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

(Which one is correct below)

• 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.)

Test statistic = 

e-2. Find the p-value.

(Which one is correct below)

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

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

(Which one is correct below)

• 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. 
(Which one is correct below)

• 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.