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A stock analyst wants to determine whether there is a difference in the mean rate of return for three types of stock: utility, retail, and banking stocks. The following output is obtained:

Picture

a. http://ezto.mheducation.com/13252703214728584664.tp4?REQUEST=SHOWmedia&media=lind16e.png
Using the .05 level of significance, is there a difference in the mean rate of return among the three types of stock?

Yes, since the test statistic is greater than the critical value What is the critical value?
.

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Solution Summary

The expert calculates and interprets F-statistics in two-way ANOVA.

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In the example shown in the attached picture, there is indeed a difference in the means of the three stocks. The F-statistic (the test statistic) is 15.61. To obtain the critical value of F, since it's not given in the output - most programs will show it for you) you need to consult a table of critical values of F for various degrees of freedom (df) combinations. A good one is at http://www.itl.nist.gov/div898/handbook/eda/section3/eda3673.htm:

Upper critical values of the F distribution
for ?1 numerator degrees of freedom and ?2 denominator degrees of freedom

5% significance level

F.05(?1,?2)

?1 1 2 3 4 5 6 7 8 9 10
?2

1 161.448 199.500 215.707 224.583 230.162 233.986 236.768 238.882 240.543 241.882
2 18.513 19.000 19.164 19.247 19.296 19.330 19.353 19.371 19.385 19.396
3 10.128 9.552 9.277 9.117 9.013 8.941 8.887 8.845 8.812 8.786
4 7.709 6.944 6.591 6.388 6.256 6.163 6.094 6.041 5.999 5.964
5 6.608 5.786 5.409 5.192 5.050 4.950 4.876 4.818 4.772 4.735
6 5.987 5.143 4.757 4.534 ...

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