Howdy! I'm Professor Curtis of Aspire Mountain Academy here with more statistics homework help. Today we're going to learn how to apply goodness of fit hypothesis testing to horse race pole [post] positions. Here's our problem statement: The table below lists the frequency of wins for different post positions in a horse race. A post position of 1 is closest to the inside rail, so that horse has the shortest distance to run. Because the number of horses varies from year to year, only the first 10 posts positions are included. Use a 5% significance level to test the claim that the likelihood of winning is the same for the different post positions. Based on the result, should betters consider the post position of a horse race?
OK, the first part of this problem asks us to determine the null and alternative hypothesis. What we're conducting here is a goodness of fit test, because we've got these positions here for the different horses, and they were testing the claim of the likelihood of winning being the same for each of the different posts positions. So because the claim is that everything is the same, and we've got more than just two elements that we're looking at here, that's going to indicate goodness of fit hypothesis testing.
When you have goodness of fit hypothesis testing, the null hypothesis is always the same. And it is that everything is equal; everything is the same. So here we're going to look at the different options and select the one that has what we want in it, which is that everything is the same. "Wins occur with equal frequency" --- that's the one we want.
The alternative hypothesis will then be one of two things: it either conforms to some given distribution, or, in this case since we're not asked to conform to a distribution, the alternative hypothesis will be that at least one of your elements is different from the others. So at least one post position has a different frequency. Fantastic!
Now the second part asks for the chi square test statistic. So to do this, I'm going to take the data and dump it into StatCrunch. OK, here's my data. It's in StatCrunch. I'm going to resize this window so we can see everything a bit better. Now to conduct the actual test, I'm going to go into Stat, and then come down here to Goodness of fit --> Chi square test (because we're looking for a chi square test statistic).
You can see down here that I need to put in values for the observed and expected values. Here in the observed, I want to select the frequencies that we've seen with the different posts positions. Expected --- I can either put in a column that has values from a given distribution or, since that's not the case here, I'm going to select All cells in equal proportion. And I'm ready to hit Compute!, and there is my chi square test statistic, which I'm asked to round to three decimal places. Well done!
The next part asks us to calculate the P-value, which we've already done. It's right next to the test statistic there. That last value there in the results window rounded to four decimal places. Conveniently, that's what I'm given here in my answer window. Fantastic!
What is the conclusion for this hypothesis test? Well, we were asked to use a 5% significance level to test our claim. Our P-value over here, 10%, is greater than 5%, so we're outside the region of rejection, and therefore we fail to reject the null hypothesis. Every time we fail to reject the null hypothesis, there is insufficient evidence. So we're going to want this answer option here. Nice work!
And the last part of this question asks, "Based on the results should betters consider the post position of a horse race?" Well, what do we conclude from our hypothesis test? We failed to reject H naught, which means that H naught could be true. What was H naught? Well, scroll back up here, and we see that H naught, our null hypothesis, is that wins occur with equal frequency. Well, if they're occurring with equal frequency, and this statement is potentially true, then it shouldn't be a consideration when you're placing your bet. So here I'm going to select No. Well done!
And that's how we do it at Aspire Mountain Academy. Be sure to leave your comments below and let us know how good a job we did or how we can improve. And if your stats teacher is boring or just doesn't want to help you learn stats, go to aspiremountainacademy.com, where you can learn more about accessing our lecture videos or provide feedback on what you'd like to see. Thanks for watching! We'll see you in the next video.
Frustrated with a particular MyStatLab/MyMathLab homework problem? No worries! I'm Professor Curtis, and I'm here to help.