## Question 866:

1

1. Q866_1_q866.xls
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.

1. 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.
2. Next add 1 divided by each sample size = 1/3303 +1/3303 = .0061.
3. Multiply the results from steps 1 and 2 then take the square root = SQRT(.0061*.02907) = .004196
4. The test statistic is the difference divided by the result from step 3 = .01150/.004196 = 2.74195
5. Looking up this value in a normal table we get a 2-sided p-value of .00611.
Since the p-value is less than .01 we reject the Null hypothesis and conclude that the incidence of cancer is greater in DES users.

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.