A study of potential age discrimination considers promotions among managers in a large company. The data are given in the table below. You have to test at a 1% level of significance whether a significant relation between age and promotions exists.
Age
Under 30
30 – 39
40 – 49
50 and over/en meer
Promoted
9 (A)
29 (B)
32 (C)
10 (D)
Not promoted
41 (E)
41 (F)
48 (G)
40 (H)
Calculate the expected value (G)
0.19
0.32
0.68
1.0
54.4
56.2
The expected value (G) can be calculated using the formula:
G = (total number of promotions) * (total number of individuals in the age group) / (total number of individuals)
G = (9 + 29 + 32 + 10) * (48 + 40 + 41 + 41) / (9 + 29 + 32 + 10 + 48 + 40 + 41 + 41)
G = 80 * 170 / 250
G = 13.6
Therefore, the expected value (G) is 13.6.
To calculate the expected value (G) in this case, we need to use the formula:
Expected Value = (Sum of row totals * Sum of column totals) / Grand total
First, let's calculate the row totals and column totals:
Row total for Promoted = A + B + C + D = 9 + 29 + 32 + 10 = 80
Row total for Not promoted = E + F + G + H = 41 + 41 + 48 + 40 = 170
Column total for Age (Under 30) = A + E = 9 + 41 = 50
Column total for Age (30-39) = B + F = 29 + 41 = 70
Column total for Age (40-49) = C + G = 32 + 48 = 80
Column total for Age (50 and over) = D + H = 10 + 40 = 50
Grand total = Sum of all values = A + B + C + D + E + F + G + H = 9 + 29 + 32 + 10 + 41 + 41 + 48 + 40 = 250
Now, let's calculate the expected value:
Expected Value = (Row total for Promoted * Column total for Age (40-49)) / Grand total
= (80 * 80) / 250
= 6400 / 250
= 25.6
Therefore, the expected value (G) is approximately 25.6.
To calculate the expected value (G), we need to calculate the expected number of promotions for each age category. The expected number of promotions can be calculated using the formula:
Expected number of promotions = (Total number of promotions / Total number of managers) * Number of managers in each age category
Total number of promotions = 9 + 29 + 32 + 10 = 80
Total number of managers = 9 + 29 + 32 + 10 + 41 + 41 + 48 + 40 = 250
Now, let's calculate the expected number of promotions for each age category:
For the "Under 30" category:
Expected number of promotions = (80/250) * 50 = 0.16 * 50 = 8
For the "30 - 39" category:
Expected number of promotions = (80/250) * 70 = 0.32 * 70 = 22.4
For the "40 - 49" category:
Expected number of promotions = (80/250) * 80 = 0.32 * 80 = 25.6
For the "50 and over" category:
Expected number of promotions = (80/250) * 50 = 0.16 * 50 = 8
Now, let's calculate the overall expected value (G):
Expected value (G) = Sum of all expected number of promotions = 8 + 22.4 + 25.6 + 8 = 64
Therefore, the expected value (G) is 64.