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A company wants to determine if its employees have any preference among 5 different health plans which it offers to them. A sample of 200 employees provided the data below. Calculate the chi-square test statistic to test the claim that the probabilities show no preference. Use alpha = 0.01.
Plan 1 2 3 4 5
Employees 30 55 18 32 65
a. 37.45
b. 55.63
c. 45.91
d. 48.91

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Answer:

37.45

Explanation:

Given the data:

Plan 1 2 3 4 5

Employees (X) : 30 55 18 32 65

α = 0.01

Sample size (n) = 200

Preference among 5 different health plans

Expected value of data (E) :

Sum of employees / number of plans

= (30 + 55 + 18 + 32 + 65) / 5 = 40

Σ((X - E)^2 / E)

(((30 - 40)^2) / 40) + (((55 - 40)^2) / 40) + (((18 - 40)^2) / 40) + (((32 - 40)^2) / 40) + (((65 - 40)^2) / 40) = 37.45

Hence, the Chi square Test statistic = 37.45