Question

In: Statistics and Probability

Use the provided contingency table and expected frequencies. At alpha equals 0.01​, test the hypothesis that...

Use the provided contingency table and expected frequencies. At alpha equals 0.01​, test the hypothesis that the variables are independent. What is the test statistic?

Result stretched not stretched
injury 16(20.979) 24(19.021)
No injury 209(204.021) 180(184.979)

Solutions

Expert Solution

The following is the table for observed and expected frequency

Result stretched not stretched
injury 16(20.979) 24(19.021)
No injury 209(204.021) 180(184.979)
Observed Frequency(O) Expected Frequency ( E) ( O-E)^2 ( O-E)^2/E
16 20.979 24.790441 1.181678869
24 19.021 24.790441 1.303319542
209 204.021 24.790441 0.121509261
180 184.979 24.790441 0.134017597
429 429 99.161764 2.740525269

= 2.74

Null hypothesis: the events are independent

Alternate hypothesis: the events are dependent

The critical value at df = 4 - 1 = 3 and alpha = 0.01 is given by = 11.345

Reject the null hypothesis if >

Here, = 2.74 < = 11.345

Hence do not reject the null hypothesis

The events are independent

orchestra answered 1 year ago
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