How productive are U.S. workers? One way to answer this question is to study annual pro­ts per employee. A random sample of companies in computers (I), aerospace (II), heavy equipment (III), and broadcasting (IV) gave the following data regarding annual pro­ts per employee (units in thousands of dollars) (Source: Forbes Top Companies, edited by J. T. Davis, John Wiley and Sons).

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

In each problem, please provide the following information.

(a) What is the level of signifi­cance? State the null and alternate hypotheses.

(b) Find SS_TOT, SS_BET, and SSW and check that SS_TOT – SSB_ET + SS_W. Find d.f._BET, d.f._W, MS_BET, and MS_W. Find the value of the sample test statistic F (F ratio).

What are the degrees of freedom?

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

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

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

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

193210 IV 764509 39280 20727 397663 II 391869 88189 173481 221 1