Answer 11) 0
If the null hypothesis is true, then the observed and expected frequencies will be equal in value. As a result, the χ2 statistic will be equal to zero.
Answer 12) 69.8601
Expected Value of a Cell = (Row Total)*(Column Total)/Total No. of Observations
Row Total for Underarm brace treatment = 111
Column Total for success = 180
Total no. of observations = 286
Expected Value = (111*180)/286
Expected Value = 69.8601
Answer 13) 2.8620
The formula for contribution = (Observed value - Expected value )^2/Expected value
In this case, Observed value = 84
Expected value = 69.8601 (Refer to Answer 12)
Contirbution = (84 - 69.8601)^2/69.8601
Contirbution = 2.8620
Answer 14) 0.0018
Given χ2 = 12.6266
Degrees of Freedom = (r-1)*(c-1) = (3-1)*(2-1) = 2
P-value corresponding to χ2 = 12.6266 and df = 2 is 0.0018 (Obtained using p-value calculator. Screenshot below)
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