Finding a sample proportion and the corresponding confidence interval

Intro

Howdy!  I'm Professor Curtis of Aspire Mountain Academy here with more statistics homework help.  Today we're going to learn how to find a sample proportion and the corresponding confidence interval.  Here's our problem statement: In a survey of 3363 adults aged 57 through eighty five years, it was found that 89.4% of them used at least one prescription medication.  Complete Parts A through C below.

Part A

OK, Part A asks how many of the 3363 subjects used at least one prescription medication.  This is easily answered with the help of a calculator, so I'm going to pull out my calculator here.  And all I need to do is take the total number that I'm given and multiply it by the proportion that I'm looking for.  In order to use this percent in a calculation, I need to convert it to decimal.  So the first thing I'm going to do is put in the total number 3363 and multiply it by the proportion, convert it to a decimal form so I have to move that decimal point over two places to the left.  And here I have my answer.

Now what I need to provide is an actual whole number, because you don't count partial people; you only count whole people.  At least, I hope you're not counting partial people!  Here our instructions say, “Round to the nearest integer as needed.”  So I'm just going to follow the regular rules of rounding here.  I got 0.522; that means I'm going to round this number up to 3007.  Excellent!

Part B

And now, Part B asks us to “construct a 90% confidence interval estimate of the percentage of adults aged 57 through 85 years who use at least one prescription medication.”  This is most easily accomplished in StatCrunch, so I'm going to pull up my StatCrunch window.

Notice I have StatCrunch opened in a separate window.  I often do this when I'm working these problems because you never know when you're going to need it, and they don't actually give you any sort of icon here inside the problem for you to open up StatCrunch.  I could go up here to Question Help, and then here StatCrunch is an option here.   But I always like to just keep it separate in a window so I'm sure that I absolutely have it.

To construct a confidence interval estimate, we don't need any actual data; we have summary stats here in our problem statement.  So I'm going to go up to Stat –> Proportion Stats (because I'm constructing a confidence interval on proportions) –> One Sample (because I'm only given one sample), and then I want to select With Summary because I don't have actual data to use; I only have summary statistics.

Now here in my options window, the first thing I need to do is determine the number of successes.  This is simply the proportion that they're going to give you in the actual problem statement.  But you need to enter it as a whole number.  We calculated that in the previous part of the problem — 3007.  The number of observations is the total number that's in the sample.  That's this number here.  Then I click on the radio button for confidence interval and make sure that I have the right confidence level in the confidence level field.

Once I have that put in, all the other defaults are fine, so I press Compute! and out comes my results window with these two numbers on the end — the upper and lower limits for my confidence intervals.  Notice, however, that the answer fields have a percent after them.  That means I have to convert these numbers from decimal to percent, so I have to move the decimal point two places over.  Then I put my answer in.  So this first one is going to be 88.5, and the second one is going to be 90.3.  I check my answer.  Excellent!

Part C

Now Part C asks, “What do the results tell us about the proportion of college students who use at least one prescription medication?”  Well, go back and look at the actual data that we have collected.  We have adults aged 57 through 85 years.  But the question is asking us about college students, so how representative of that population is our sample?  In other words, how many college students are we gonna find in a sample of people aged 57 through 85 years?  The answer is you might find a few; there are some older individuals who go back to college just for their own personal enrichment.  They're not looking for any sort of career, but you're not gonna find a whole lot.

So no more than a small handful of people in that sample are actually going to be college students.  That means our sample is not representative of the population that we're interested in.  And therefore it can't really tell us very much.  Remember, in order to make conclusions about a about a population from a sample, that sample needs to be representative and characteristic of the population.  Here we don't have that connection.  Therefore, the conclusions we make about this sample should not be applied to that population.

The answer option that best matches that conclusion here is Answer Option A, “The results tell us nothing.”  I check the answer.  Good job!

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