Question

# How productive are U.S. workers? One way to answer this question is to study annual profits...

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

# part -f

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