Thread: Point estimate for the true population proportion

The article “Ban on Smoking Show to Improve Lung Health” (Los Angeles Times, December 9, 1998) reported the results of a study of San Francisco bartenders. Of 39 bartenders who reported respiratory problems before a ban on smoking in bars, 21 were symptom-free 2 months after the ban began. Suppose that it is reasonable to regard this group of 39 bartenders as a random sample of bartenders with reported respiratory problems. Assuming that there are more than 400 bartenders with respiratory problems, use this information to:

a) Obtain a point estimate (from the sample) for the true population proportion of bartenders who reported respiratory problems before a ban on smoking in bars who were symptom-free 2 months after the ban began.


Wouldn't the answer to this be 21 since the problem states that 21 were symptom-free 2 months after the ban? It just seems like such a small number when they then say that there are more than 400 bartenders with respiratory problems but I researched the problem a bit and found an example that says, "The mean running time of a random sample of 12-year-olds would be an estimate of the mean running time for all 12-year-olds.". Would 21 be the correct answer?

Alright, I asked my professor about it and he basically said no, that's not the answer. I asked if I should turn it into a percentage by doing 21/39 but I'm still a bit confused. I think he said it should be a number between 0 and 1 and doing that would give me .54 which is between 0 and 1. I might have that wrong though because I was a bit flustered when I went to see him, I've been running all over the building looking for a lab to work in. >.<