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Question
200 teenagers were asked which take-out food do they prefer - French fries, burger, or pizza. The results were -
| French fries | Burger | Pizza | |
| Boys | 6 | 20 | 24 |
| Girls | 18 | 40 | 92 |
Compute χ2 Statistics.
Solution
Table of observed frequencies.
| French fries | Burger | Pizza | Row total (Ri) | |
| Boys | 6 | 20 | 24 | 50 |
| Girls | 18 | 40 | 92 | 150 |
| Column total (Cj) | 24 | 60 | 116 | 200 |
Expected frequencies are given by
Eij = `("R"_"i"×"C"_"j")/"N"`
E11 = `(50xx24)/200` = 6
E12 = `(50xx60)/200` = 15
E13 = `(50xx116)/200` = 29
E21 = `(150xx24)/200` = 18
E22 = `(150xx60)/200` = 45
E23 = `(150xx116)/200` = 87
Table of expected frequencies.
| French fries | Burger | Pizza | Total | |
| Boys | 6 | 15 | 29 | 50 |
| Girls | 18 | 45 | 87 | 150 |
| Total | 24 | 60 | 116 | 200 |
Now,
χ2 = `sum[(("O"_"ij" - "E"_"ij")^2)/"E"_"il"]`
= `((6 - 6)^2)/(6) + ((20 - 15)^2)/(15) + ((24 - 29)^2)/(29) + ((18 - 18)^2)/(18) + ((40 - 45)^2)/(45) + ((92 - 87)^2)/(87)`
= `0 + (25)/(15) + (25)/(29) + 0 + (25)/(45) + (25)/(87)`
= 1.67 + 0.86 + 0.56 + 0.29
= 3.38
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