Men diagnosed with prostate cancer were randomly assigned to

Men diagnosed with prostate cancer were randomly assigned to either undergo surgery or not. Among the 347 men who had surgery, 16 eventually died of prostate cancer , compared with 31 of the 348 men who did not have surgery. What is the standard error of the difference in the two proportions? And how can I do this on a TI-83 calculator?

Solution

As

x1 = 16
n1 = 347
x2 = 31
n2 = 348

Getting p1^ and p2^,          
          
p1^ = x1/n1 =    0.04610951      
p2 = x2/n2 =    0.08908046      
          
Also, the standard error of the difference is          
          
sd = sqrt[ p1 (1 - p1) / n1 + p2 (1 - p2) / n2] =    0.018971796   [ANSWER]

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You can use the 2-propztest in ti-84 to carry out a test.

However, if you really need the standard error of the difference, this is the formula. However, there is no other way around it but to use the formula.