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Q: Statistical Question ( No Answer,   2 Comments )
Question  
Subject: Statistical Question
Category: Miscellaneous
Asked by: cupid2323-ga
List Price: $10.00
Posted: 29 Dec 2005 13:07 PST
Expires: 01 Jan 2006 15:05 PST
Question ID: 611015
One reads that a business school graduate with an undergraduate degree
earns more than a high school graduate with no additional education,
and a person with a master's degree or a doctorate earns even more. To
investigate we select a sample of 25 mid-level managers of companies
with less than 200 employees. Their incomes, classified by highest
level of education, follow.

Income ($ thousands) 
High School or Less    45  47  53  62  39  43  54  
Undergraduate Degree   49  57  85  73  81  84  89  92  62 
Master's Degree or More  51  73  82  59  94  89  89  95  73 

Test at the .05 level of significance that there is no difference in
the arithmetic mean salaries of the three groups. If the null
hypothesis is rejected, conduct further tests to determine which
groups differ.
Answer  
There is no answer at this time.

Comments  
Subject: Re: Statistical Question
From: hnguyen-ga on 29 Dec 2005 22:20 PST
 
Running ANOVA, we get

          Df Sum Sq Mean Sq F value    Pr(>F)    
x          2 3872.0  1936.0  10.185 0.0007398 ***
Residuals 22 4182.0   190.1  

The p-value is .00073, much smaller than the threshold of .05, so we
can safely reject the null hypothesis that there is no difference in
the salaries of the three groups. Running further test to see which
pairs differ,

            Estimate Std. Error t value Pr(>|t|)    
(Intercept)   49.000      5.211   9.403 3.66e-09 ***
x2            25.667      6.948   3.694 0.001268 ** 
x3            29.333      6.948   4.222 0.000351 ***

From here, we know that pair 1v2 and 1v3 differ among themselves with
p-values .0012 and .00034, respectively. (1, 2, and 3 are categorical
variables corresponding to High School, Undergraduates, and Masters'
Degree). Pair 2v3 are pretty much the same. A graphical representation
of the data above can be found here

http://www.stat.ucla.edu/~hnguyen/data.jpeg
Subject: Re: Statistical Question
From: cupid2323-ga on 30 Dec 2005 08:53 PST
 
Can this be placed in excel?? I am just having a hard time understanding.

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