Question

# A random sample of five observations from three normally distributed populations produced the following data: (You...

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 15 22 17 23 28 29 31 18 24 32 15 23 23 25 27 x−Ax−A = 24.8 x−Bx−B = 21.6 x−Cx−C = 24.0 s2AsA2 = 48.2 s2BsB2 = 27.3 s2CsC2 = 21.0

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: μA = μB = μC; HA: Not all population means are equal.

• H0: μAμBμC; HA: Not all population means are equal.

• H0: μAμBμC; 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.

• 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.