Hypothesis Testing Problem

A tax preparation firm is interested in comparing quality of work of two offices. Office A - out of 250 tax returns, 35 have errors. Office B - out of 300 tax returns, 27 have errors. Test hypothesis that the proportion of erroneous return are equal at 1% level.

Does the test statistic become [(X1 bar - X2 bar) - (mu1 - mu2)] /sqrt[(sigma1^2/n1) + (sigma2^2/n2)] ~ N(0,1) ?
Considering H0 : mu1 - mu2 = 0 and H1 : mu1 - mu2 not equal to 0
then we need to put X1 bar = sigma1 = 35/250 = 0.14 and X2 bar = sigma2 = 27/300 = 0.09, n1 = 250, n2 = 300, (mu1 - mu2) =0 in test statistic? Then I am getting 4.87 as T.S. But in the answer T.S. is given as 1.87. How???

 

You are testing for equality of means
It should be tested for equality of proportion .

 

Thank you very much. But where are you finding this formula of test statistics? I'm confused! I am attaching the summary of all formulae of that chapter. Are you using 2-sample binomial one? But you have used a different p and q here.

 

Dear Sir,
I am so sorry. Actually I just memorized the summary of chap 11 and was using it in chap 12 too, since there are few differences in specific cases. However, I used an alternate formula to solve the mentioned question. Please ref. to the formula in the picture attached. Will it be considered as wrong if I use this alternate formula is exam? I am using the alternate formula because it is easier to remember, as it has similarity with chap 11 formulae. (The rejection/acceptance of null hypothesis verdict is coming the same in both the cases if I use either of these formulae but only the test statistic's value is getting differed a bit after decimal).

 

Ok sir. Thank you for your reply. I'll stick to the study material's formula only, since I can not take the risk of losing marks in the exam.