Statistical Inference Problem

Stanlex

Hi all, apologies if this is in the wrong thread, I really didn't know where to put it.

I am studying for an exam in Quantitative Analysis and I am looking through past exam papers.



I understand all of the questions but I have a slight issue. It asks for standard error for proportion which is √pq/n and then asks what correction factor would apply if n/N > 0.05 (5%). In this case the fpc, or finite population correction factor would apply. √(N-n)/(N-1)

Now, in the next part it asks you to calculate proportion of all employees who would participate in the dental plan. This is 137/200 employees. This means that n/N is greater than 5%. So would I apply the fpc here and how would I do it?

Thanks

MathsManiac

I think it would have been better to post this in the maths forum.

Anyway, to answer your question, in part 2(b)(i), n/N is not 137/200, so you are not correct in asserting that n/N > 0.05.

In this case, the sample size is n = 200. The population size is unspecified, but the context and phrasing of the question - in particular the fact that the population size is not given - suggests that that should be considered "large" (i.e., no finite-population correction, which you couldn't apply anyway as N is unknown.) They really should have been more clear on this point in the question - for example, by saying a "large company" or some such phrase.

Having said that, part (b)(ii) says that there are only 350 female employees in total in the company, so unless the workforce is very gender-imbalanced, the question is poorly constructed. The very first part of the question suggests that your lecturer expects you to consider a finite-population correction to be necessary whenever n/N > 0.05. Since you clearly can't apply it in part (b)(i), there's an inherent assumption in the question that this company has at least 4000 employees. To leave this as an unstated but necessary assumption and then moments later state that there are 350 female employees is disconcerting.

Stanlex

MathsManiac wrote: »

I think it would have been better to post this in the maths forum.

Anyway, to answer your question, in part 2(b)(i), n/N is not 137/200, so you are not correct in asserting that n/N > 0.05.

In this case, the sample size is n = 200. The population size is unspecified, but the context and phrasing of the question - in particular the fact that the population size is not given - suggests that that should be considered "large" (i.e., no finite-population correction, which you couldn't apply anyway as N is unknown.) They really should have been more clear on this point in the question - for example, by saying a "large company" or some such phrase.

Having said that, part (b)(ii) says that there are only 350 female employees in total in the company, so unless the workforce is very gender-imbalanced, the question is poorly constructed. The very first part of the question suggests that your lecturer expects you to consider a finite-population correction to be necessary whenever n/N > 0.05. Since you clearly can't apply it in part (b)(i), there's an inherent assumption in the question that this company has at least 4000 employees. To leave this as an unstated but necessary assumption and then moments later state that there are 350 female employees is disconcerting.

Thanks for the reply. Definitely cleared it up.