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5.  We want to estimate the average burning time for our particular\\
\ \ \ \ statistics book.  We go out and burn 15 and find the sample mean to be\\
\ \ \ \ 17.4 minutes with a sample standard deviation of 2.3 minutes.  What is a\\
\ \ \ \ 80\% confidence interval for the actual mean burning time?\\
\ \\
6. Through much effort, we manage to catch 4 terrapins and measure their\\
\ \ \ \ shell diameters to be (in inches):
$$10.2\;\; 14.7\;\; 11.6\;\; 13.1\;\;$$
\ \ \ \ Give a 90\% confidence interval for the actual mean shell diameter.\\
\ \\
7. Bill, an evil quality control engineer wants to insure that all of the\\
\ \ \ \ crayons he makes have approximately the same amount of lead.  To do\\
\ \ \ \ this he wants to estimate the standard deviation.  He selects 17\\
\ \ \ \ crayons at random off the production line, and calculates the sample\\
\ \ \ \ standard deviation of amount of lead contained in the crayons to be\\
\ \ \ \ $.06$ mg.  What is a 95\% confidence interval for the actual standard\\
\ \ \ \ deviation?

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