Subtract each corresponding expected value from list too square that difference before dividing by the expected value from list, too, and we will get these decimals. We want to calculate calculator to generate these values, so we're going to tell the calculator to take each observed value from list one. So for list three, we're going to sit up on top. I've already placed the observed frequencies and enlist to I have placed the expected value off 33 a third. Three before we start and I'm going to go to stat edit and, as you can see, enlist one. So I'm going to bring in my graphing calculator, and I am going to clear out my list. And the fastest, most efficient way to handle this is to utilize a graphing calculator. I'm going to square and then I'm going to divide it by the expected value or the expected frequency. So I'm going to take the observed data for one. I'm going to extend out my chart, and this time I need to calculate the observed, minus the expected quantity squared, divided by expected. So we're now ready to come up with our Chi Square test statistic. So our expected frequencies for each number should be 33 1 3rd. So if we take that 200 we divide it by the six possible values, we will get 33 a third. Now, If this was a fair die, we would expect an equal number of ones twos, threes and so forth. Now we know that we rolled 200 times, so if you add up the observed frequencies, you are going to get 200. So let's go back to our chart, see what we have and see what we need. The sum of observed minus, expected squared, divided by expected. And in order to do so, we're going to apply the formula. So in order to run the goodness of fit test, we are going to have to calculate the Chi Square test statistic for this data. So we're going to be running a goodness of fit test to see how well or if the actual observed roles fit what is expected And if they don't fit what is expected when you roll a normal die, then we're going to support this claim. So we're going to say that are null hypothesis are that the outcomes are equally likely and our alternative hypothesis will be that the outcomes are not equally likely. Now you are no hypothesis are always that the outcomes fit the expected values. So before we can run the hypothesis test, we're going to have to create a no hypothesis and an alternative hypothesis. So we want to run a hypothesis test at a 0.5 significance level to test a claim, and our claim is that the outcomes are not equally likely due to the lead weight being put into the die. So those air referred to as are observed frequencies. And the frequencies were 27 31 42 40 28 and 32. And in this particular problem, the author is drilling a hole in the dye and fills it with a lead weight and then rolls it 200 times and observes the frequencies. The outcomes on a die are normally one to three, four, five or six.
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