Allied Corporation wants to increase the productivity of its line workers. Four

Question

Allied Corporation wants to increase the productivity of its line workers. Four different programs have been suggested to help increase productivity. Twenty employees, making up a sample, have been randomly assigned to one of the four programs and their output for a day's work has been recorded. You are given the results below.

   Program A   Program B   Program C   Program D

   150   150   185   175

   130   120   220   150

   120   135   190   120

   180   160   180   130

   145   110   175   175

A) State the null and alternative hypotheses. B) Construct an ANOVA table.C) As the statistical consultant to Allied, what would you advise them? Use a .05 level of significance. Use both the critical and p-value approaches. D) Use Fisher's LSD procedure and determine which population mean (if any) is different from the others. Let = .05.

Explanation / Answer

answer a) null hypothesis Ho: there is no difference of output among all four program

alternative hypothesis H1: at least two program differ among four program

ANOVA

look anova table carefully

critical value of F(3,12)=3.49 , calculated F=2.83

since the calculated F-value 2.83 is less than critical F=3.49 so we accept null hypothesis

in other way also the p-value 0.0544 is more than the alpha=0.05 we accept null hypotheis

d) LSD=sqrt(2*MSE/r)*t-value(error df)=sqrt(2*513.54/5)*t(0.05,12)=sqrt(205.42)*2.18=31.23

Source DF Sum of Squares Mean Square F Value Pr > F Model 7 10187.50000 1455.35714 2.83 0.0544 Error 12 6162.50000 513.54167 Corrected Total 19 16350.00000

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