The following data are from an experiment designed to investigate the perception
ID: 3175531 • Letter: T
Question
The following data are from an experiment designed to investigate the perception of corporate ethical values among individuals who are in marketing. Three groups are considered: management, research and advertising (higher scores indicate higher ethical values).
A. Compute the values identified below (to 1 decimal, if necessary).
B. Use = .05 to test for a significant difference in perception among the three groups.
Calculate the value of the test statistic (to 2 decimals).
The p-value is Selectless than .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 6
What is your conclusion?
SelectConclude the mean perception scores for the three groups are not all the sameCannot conclude there are differences among the mean perception scores for the three groupsItem 7
Explanation / Answer
A. Complete the following table:
Xbar=(6+3.5+8)/3
=5.83
SST=Sigma Xi^2-NXbar^2
=(220+75+386)-18*5.83^2
=69.1998
SSTr=Sigma Nk (Xbark-Xbar)^2
=6(6-5.83)^2+6(3.5-5.83)^2+6(8-5.83)^2
=61.0002 (ans)
SSE=SST-SSB=69.1998-61.0002=8.1996 (ans)
MSE=SSW/dfW=8.1996/(N-k)=8.1996/(18-3)=0.54664 (ans)
MSTr=SSB/dfB=61.0002/(k-1)=61.0002/(3-1)=30.5001 (ans)
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F=MSTr/MSE
=30.5/0.5
=61
For a higher F value, p value is less than 0.01.
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Reject H0, if p value is less than 0.05. Here, p value is less than 0.05, therefore, reject H0, and conclude that atleast mean perception score of one group is significnatly different from another. Option 1.
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LSD=tcritical*sp*sqrt(1/n1+1/n2), where, sp is pooled standard deviation, and is computed as sqrt MSE, t critical is obtained at 95% c.i and N-k degrees of freedom, and n1 and n2 denotes sample size for group1 and group2 respectively.
If two group means differ by more than this amount, then they are significantly different at level alpha for each individual test.
LSD1-2=1.75*(sqrt 0.5)sqrt (1/6+1/6)
=0.7144
Now compute absolute difference and compare it with the LSD.
x1-x2=(6-3.5)=2.5 >0.7144 (perception scores for marketing managers and marketing research is significantly different).
x1-x3=(6-8)=-2< 0.7144 (perception scores for marketing managers and advertising is not significantly different).
x2-x3=(3.5-8)=-4.5 <0.7144 (perception scores for marketing research and advertising is not significantly different).
Marketing manager Marketing research Advertising 7 49 4 16 8 64 6 36 4 16 9 81 5 25 3 9 8 64 6 36 3 9 7 49 7 49 4 16 8 64 5 25 3 9 8 64 x1bar=36/6=6 Total:220 x2bar=21/6=3.5 Total:75 x3bar=48/6=8 Total:386Xbar=(6+3.5+8)/3
=5.83
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