Question

alan is a physical therapist who specializes in leg injuries. His patients differ in age and type of injury. 0-12 years old 13-19 years old 14 Knee pain 9 13 3 Ankle pain 6 9 Quadricep pain 9 6 Shin pain re the events "the patient suffers from knee pain" and "the patient is 13-19 years old" independent? no yes

Answer 1

0-12 years 13-19 years Total

Knee 14 9 23

Ankle 13 3 16

Quadricep 6 9 15

Shin 9 6 15

________________________________________

Total 42 27 69

Now we can calculate the chi square statistic given by:

`\chi^2=\sum ^n_(i=1)((O-E)^2)/(E)`

The expected values for this case are:

0-12 years 13-19 years Total

Knee 14 9 23

Ankle 9.74 6.26 16

Quadricep 9.13 5.87 15

Shin 9.13 5.87 15

________________________________________

Total 42 27 69

Then the statistic is given by:

`\chi^2=((14-14)^2)/(14)+((9-9)^2)/(9)+((13-9.74)^2)/(9.74)+((3-6.26)^2)/(6.26)+((6-9.13)^2)/(9.13)+((9-5.87)^2)/(5.87)+((9-9.13)^2)/(9.13)+((6-5.87)^2)/(5.87)`

Solving we got:

`\chi^2=1.09+1.70+1.07+1.67+0.00185+0.0028=5.53`

The degrees of freedom are given by:

df = (2-1)*(4-1)= 3

And the p value is given by:

p = P(X > 5.53) = 0.137

Since the p value is higher than 0.05 we can conclude that we fail to reject the null hypothesis of independence

So then the correct answer is:

yes