Question

How productive are U.S. workers? One way to answer this question is to study annual profits per employee. A random sample of companies in computers (I), aerospace (II), heavy equipment (III), and broadcasting (IV) gave the following data regarding annual profits per employee (units in thousands of dollars).

I (27.6;23.1;14.7;8.9;11.9)

II (13.1;9.9;11.7;8.1;6.9;19.5)

III ( 22.4;20.2;7.4;12.9;7.7)

IV (17.6;16.8;14.4;15.7;10.7;9.4)

Shall we reject or not reject the claim that there is no difference in population mean annual profits per employee in each of the four types of companies? Use a 5% level of significance.

(a) What is the level of significance?

State the null and alternate hypotheses.

Ho: μ1 = μ2 = μ3 = μ4; H1: Not all the means are equal.

Ho: μ1 = μ2 = μ3 = μ4; H1: All four means are different.

Ho: μ1 = μ2 = μ3 = μ4; H1: Exactly two means are equal.

Ho: μ1 = μ2 = μ3 = μ4; H1: Exactly three means are equal.

(b) Find

SSTOT,SSBET and SSW and check that SSTOT = SSBET + SSW. (Use 3 decimal places.)

SSTOT =

SSBET =

SSW =

Find d.f.BET, d.f.W, MSBET, and MSW. (Use 3 decimal places for MSBET, and MSW.)

dfBET =

dfW =

MSBET =

MSW =

Find the value of the sample F statistic. (Use 3 decimal places.)

What are the degrees of freedom?

(numerator)

(denominator)

(c) Find the P-value of the sample test statistic.

P-value > 0.100

0.050 < P-value < 0.100

0.025 < P-value < 0.050

0.010 < P-value < 0.025

0.001 < P-value < 0.010

P-value < 0.001

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?

Since the P-value is greater than the level of significance at α = 0.05, we do not reject H0.

Since the P-value is less than or equal to the level of significance at α = 0.05, we reject H0.

Since the P-value is greater than the level of significance at α = 0.05, we reject H0.

Since the P-value is less than or equal to the level of significance at α = 0.05, we do not reject H0.

(e) Interpret your conclusion in the context of the application.

At the 5% level of significance there is insufficient evidence to conclude that the means are not all equal.

At the 5% level of significance there is sufficient evidence to conclude that the means are all equal.

At the 5% level of significance there is insufficient evidence to conclude that the means are all equal.

At the 5% level of significance there is sufficient evidence to conclude that the means are not all equal.

(f) Make a summary table for your ANOVA test.

Source of Variation Sum of Squares Degrees of Freedom MS F Ratio P Value Test Decision Between groups Within groups Total

Answer 1

# part -f