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 25 17 22 25 19 26 27 25 26 32 18 30 18 17 27 x−Ax−A = 25.4 x−Bx−B = 19.2 x−Cx−C = 26.2 s2AsA2 = 25.3 s2BsB2 = 11.2 s2CsC2 = 8.2

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.

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

• p-value 0.10
• 0.05 p-value < 0.10

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.

 Applying one way ANOVA: (use excel: data: data analysis: one way ANOVA: select Array):
 Source SS df MS F P value Fcrit Between 146.80 2 73.400 4.926 0.027 3.885 Within 178.80 12 14.9000 Total 325.60 14

a)

grand mean =23.60

b)

SSTR=146.80

MSTR =73.40

c)

SSE =178.80

MSE =14.90

d)

H0: μA = μB = μC; HA: Not all population means are equal.

e)

0.025 p-value < 0.05

f)

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

g)

We conclude that some means differ.