A study of potential age discrimination considers promotions among middle manage
ID: 3292625 • Letter: A
Question
A study of potential age discrimination considers promotions among middle managers in a large company. The data are as follows: The data set is called PROB5.sav.
Age Under 30 30 - 39 40 - 49 50 and Over Total
Promoted 9 29 32 10 80
Not Promoted 41 41 48 40 170
Totals 50 70 80 50 250
a. Find the expected numbers in each cell for the promoted row under the hypothesis of independence of age and promoted for the row Promoted. Neatly write the expected value to two decimals inside the cells in the table above.
b. Justify the indicated degrees of freedom.
c. What is the Chi Square value for the cell where Not Promoted and 40 – 49 come together (The (2 , 3) cell?
d. Reject the null hypothesis if x2 cal > x2 .10/1 , / (write in the degrees of freedom value)
e. Is there significant evidence of a relation between age and promotion? . Show the SPSS output that supports your answer.
f. What is the p-value and the conclusion? P-value = ___________________
Explanation / Answer
a)
b) df = (r-1)(c-1) = 3
c) Chi Square value for the cell where Not Promoted and 40 – 49 come together = 54.4
d)
for alpha= 0.10
critical value = 6.25
hence reject if TS> 6.25
e)
since TS = 13.025 > 6.25
we reject the null
there is significant evidence of a relation between age and promotion
f)
p-value = P(X^2 > 13.02521) = 0.005
c1 c2 c3 c4 sum r1 9 29 32 10 80 r2 41 41 48 40 170 sum 50 70 80 50 250 Eij 1 2 3 4 expected 1 16 22.4 25.6 16 2 34 47.6 54.4 34 0i 9 29 32 10 41 41 48 40 Ei 16 22.4 25.6 16 34 47.6 54.4 34 sum (Oi-Ei)^2/Ei 3.0625 1.944643 1.6 2.25 1.441176 0.915126 0.752941 1.058824 13.02521Related Questions
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