Performing the Kruskal-Wallis test for chest deceleration measurements

Intro

Howdy!  I'm Professor Curtis of Aspire Mountain Academy here with more statistics homework help.  Today we're going to learn how to perform the Kruskal-Wallis test for chest deceleration measurements.  Here's our problem statement: Use the following listed chest deceleration measurements (in g, where g is the force of gravity) from samples, small, midsize and large cars.  Use a 5% significance level to test the claim that the different size categories have the same median chest deceleration in the standard crash test.  Do the data suggest that larger cars are safer?

Part 1

OK, the first part of this problem asks for the null and alternative hypothesis.  With the Kruskal-Wallis test, it's pretty much standard.  The null hypothesis is going to be that all of the means or median values are going to be the same.  And the alternative hypothesis is going to be that at least one of them is different, so they're not all the same.  And let's see what we got here.  So we want equal medians, not all equal.  This looks good.  Excellent!

Part 2

Next we're asked to compute the test statistic.  StatCrunch makes this super easy.  So I'm going to dump my data here into StatCrunch.  Let's resize this window so we can see better what's going on.  OK, here in StatCrunch, I go to Stat --> Nonparametrics --> Kruskal-Wallis.  Here in my options window, I'm going to select my columns, and that's all there is to it.  Here's my test statistic.  I'm asked to round to three decimal places.  Excellent!

Part 3

The next part asks for the P-value.  We've already got that calculated.  It's right next door to the test statistic here in the results window.  Were asked to round to four decimal places.  Good job!

Part 4

And now we're asked to state our conclusion and answer this question: "Do the data suggest that larger cars are safer?"  Well, are we going to reject or fail to reject the null hypothesis?  Well, we've got a P-value of just under 5%.  Our significance level is 5%, so we're just inside the region of rejection.  But it doesn't matter whether you're in a little bit or way in; in is in.  So we're going to reject the null hypothesis, and we're going to say that there is sufficient evidence.  And what are we having sufficient evidence for?  Rejecting the claim samples are from populations with the same median, because that's what this says right up here.  We're rejecting the null hypothesis that says they all have the same median value.  Nice work!

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