Finding the sample size needed to estimate a population standard deviation

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 the sample size needed to estimate a population standard deviation.  Here's our problem statement: Assume that the sample is a simple random sample obtained from a normally distributed population of flight delays at an airport.  Use the table below to find the minimum sample size needed to be 95% confident that the sample standard deviation is within 50% of the population standard deviation.  A histogram of a sample of those arrival delays suggests that the distribution is skewed (not normal).  How does the distribution affect the sample size?

Part 1

OK, the first part asks us to provide the minimum sample size needed.  To do this, we're going to use the table provided.  There are actually calculations that you can perform to get this estimated sample size.  However, they're very complicated and complex, and so, in the interest of not over burdening the student, the textbook author has elected to provide a table.  And so you just read the number from the table.

We're looking for a 95% confidence level, and so here we want the top half of this table here ---that corresponds with 95% confidence.  The other alternative listed here is 99%, but we're not going to look at that because we want a 95% confidence level.  And then you just look for the range that you want to be in.  So here we're asked to find a sample standard deviation within 50% of the population parameter, and so we just look for 50% here.  Here's 50%.  And then we just read the number right off the table, and that's what we put here in our answer field.  Good job!

Part 2

Now, the second part says a histogram of a sample of those arrival delays suggests that the distribution is skewed (not normal).  How does the distribution affect the sample size?  Well, this estimate that we have here that we put in the previous answer field comes from this table.  And the numbers in this table were produced using those complex calculations I mentioned earlier.  Those calculations assume that the data are normally distributed.

Here we're seeing a case where our data is not normally distributed; it's skewed.  Therefore, the numbers that we have here are going to be an error because they rely on an assumption that's not true.  Therefore, the answer option that we want to select is that the estimate that we make is not likely correct because it's based on an assumption that's proven to be not true.  Nice work!

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