Hypothesis Testing Problem

[Chandrima]

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???

 

[Aditya mohan mathur]

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

 

[Chandrima]

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.

 

[John Lee]

You are in the wrong chapter - that is the summary for chapter 11 which is for confidence intervals not hypothesis tests.

 

[Chandrima]

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).

 

[John Lee]

Well the question doesn't tell you what the p values are - it only tells you that they are equal. Hence since they are equal then a pooled estimator of that more equal value will be more accurate as it uses more data. Hence the core reading goes for that.

IFoA exam questions have only used the Core Reading version. I'm not sure what will happen if another one is used.

 

[Chandrima]

Well the question doesn't tell you what the p values are - it only tells you that they are equal. Hence since they are equal then a pooled estimator of that more equal value will be more accurate as it uses more data. Hence the core reading goes for that.

IFoA exam questions have only used the Core Reading version. I'm not sure what will happen if another one is used.

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.