Evaluating reported research results for falsified data

Intro

Howdy!  I'm Professor Curtis of Aspire Mountain Academy here with more statistics homework help.  Today we're going to learn how to evaluate reported research results for falsified data.  Here's our problem statement: A researcher was once criticized for falsifying data.  Among his data were figures obtained from six groups of mice with 25 individual mice in each group.  These values were given for the percentage of successes in each group: 53%, 58%, 63% 46%, 48%, 67%.  What's wrong with those values?

Solution

OK, so we're looking at six different groups and each of these groups have 25 members to them.  So what would the percentage be, let's say, if we're looking at, say, you know, looking at one out of the 25?  What would the percentage be?  Well, here if I can just do that in my calculator, 1 out of 25 gives me 4%.  If I had 2 out of the 25, then I take 2 divided by 25 and get 8%.  If I had 3 out of the 25, I get 12%.  So we can see that we're --- we're looking at multiples of 4 here.  And these numbers that we see here that are listed as the reported percentages, these are not multiples of 4.  So therefore they cannot possibly be correct.

I could also look at this backwards and say, "Yeah, you know what?  What part of the 25 corresponds with 53%?"  So I'd take my 53%, and I multiply that by the 25.  See, I've got 13 and a quarter.  Well, I understand the 13, but what are you doing with a fourth of a mouse?  It doesn't make sense.  And you get the same thing looking at the other numbers.

So all the percentages of this session should be multiples of 4.  So we're going to take that as our answer.  I check my answer.  Nice work!

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