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
−17 −12 −12 −18 −18 −9 −13 −15 −19 −12 −7 −9 −10 −6 −5 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: 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.)
e-2. Find the p-value.
0.05
p-value < 0.10
p-value
0.10
0.025
p-value < 0.05
0.01
p-value < 0.025
p-value < 0.01
f. At the 10% significance level, what is the conclusion to the test?
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 αα = 0.10.
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
