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

I	II	III	IV
27.3	13.9	22.7	17.8
23.9	9.4	20.5	16.6
14.4	11.5	7.1	14.2
8.1	8.7	12.9	15.4
11.2	6.8	7.7	10.2
	19.2		9.5

Shall we reject or not reject the claim that there is nodifference in population mean annual profits per employee in eachof the four types of companies? Use a 5% level of significance.

(a) What is the level of significance?


State the null and alternate hypotheses.

H_o: μ₁ =μ₂ = μ₃ =μ₄; H₁: Exactly three meansare equal.H_o: μ₁ =μ₂ = μ₃ =μ₄; H₁: All four means aredifferent.     H_o:μ₁ = μ₂ =μ₃ = μ₄;H₁: Not all the means areequal.H_o: μ₁ =μ₂ = μ₃ =μ₄; H₁: Exactly two meansare equal.

(b) Find SS_TOT, SS_BET, andSS_W and check that SS_TOT =SS_BET + SS_W. (Use 3 decimal places.)

SSTOT	=
SSBET	=
SSW	=

Find d.f._BET, d.f._W,MS_BET, and MS_W. (Use 3 decimalplaces for MS_BET, andMS_W.)

dfBET	=
dfW	=
MSBET	=
MSW	=

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


What are the degrees of freedom?
(numerator)
(denominator)

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

P-value > 0.1000.050 < P-value <0.100     0.025 < P-value <0.0500.010 < P-value < 0.0250.001 <P-value < 0.010P-value < 0.001

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

Since the P-value is greater than the level ofsignificance at α = 0.05, we do not rejectH₀.Since the P-value is less than orequal to the level of significance at α = 0.05, we rejectH₀.     Since theP-value is greater than the level of significance atα = 0.05, we reject H₀.Since theP-value is less than or equal to the level of significanceat α = 0.05, we do not reject H₀.

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

At the 5% level of significance there is insufficient evidenceto conclude that the means are not all equal.At the 5% level ofsignificance there is sufficient evidence to conclude that themeans are all equal.     At the 5% levelof significance there is insufficient evidence to conclude that themeans are all equal.At the 5% level of significance there issufficient evidence to conclude that the means are not allequal.

(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					---Select--- p-value > 0.100 0.050 < p-value < 0.1000.025 < p-value < 0.050 0.010 < p-value < 0.025 0.001< p-value < 0.010 p-value < 0.001	---Select--- Do not reject H0. Reject H0.
Within groups
Total