## Question 866:

1## Answer:

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You want to compare two proportions here and can use the normal approximation to the binomial. You have an observed difference of .01150 between groups.- The test statistic is found by adding the number with breast cancer divided by the total sample size (118+80)/(3303+3303) = .02997 then multiply this value times 1-.02997 = .97003 = .02997*.97003 = .02907.
- Next add 1 divided by each sample size = 1/3303 +1/3303 = .0061.
- Multiply the results from steps 1 and 2 then take the square root = SQRT(.0061*.02907) = .004196
- The test statistic is the difference divided by the result from step 3 = .01150/.004196 = 2.74195
- Looking up this value in a normal table we get a 2-sided p-value of .00611.

Note: A 2-sided test was used in this computation (which is recommended for most computations). The 1-sided p-value of .00305 is also below .01 resulting in the same conclusion.

I've attached an excel file which contains the calculations.