Performing hypothesis testing on means of tornado lengths in StatCrunch

Intro

Howdy!  I'm Professor Curtis of Aspire Mountain Academy here with more statistics homework help.  Today we're going to learn how to use StatCrunch to perform hypothesis testing on means of tornado lengths.  Here's our problem statement: A dataset includes data from 500 random tornadoes.  The display from technology available below results from using the tornado lengths (in miles) to test the claim that the mean tornado length is greater than 2.7 miles.  Use a 5% significance level.  Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim.

Part 1

OK, the first part of our problem asks us to identify the null alternative hypotheses.  The null hypothesis is by definition a statement of equality, so looking at our answer options, we can see answer option D is not going to be correct.  Now, to select from the remaining answer options, we need to determine the correct alternative hypothesis.  And to do that, we look at the claim.  What is the claim that we're being asked to evaluate?  Well, here in the problem statement, it says we're testing the claim that the mean tornado length is greater than 2.7 miles.  So we want that mean to be greater than 2.7, and that's this answer option here.  I check my answer.  Good job!

Part 2

Now we're asked identify the test statistic.  Normally in a problem like this, we would have data and we dump it into StatCrunch, and we use StatCrunch to give us the results.  In this case, we don't need to do that, because we click on this icon, we have this display from technology which already gives us what we need.  So here's our test statistic, located here, the T stat.  We're asked to round to two decimal places.  Nice work!

Part 3

Now we’re asked for the P-value.  That's also there in that technology display, right next to the test statistic.  I'm asked to round to three decimal places.  Good job!

Part 4

And now we're asked to state the final conclusion that addresses the original claim.  We do that by comparing our P-value with our significance level.  So here's our P-value, 3.9%.  We're asked to compare that with the alpha level of 5%.   So our p-value is definitely less than our significance level.  That means we're inside the region of rejection, and therefore we reject H0. Because we reject H0, we can say that there is sufficient evidence.  Good job!

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