 Hello. This is a video about conducting a goodness-of-fit hypothesis test. You're conducting a multinomial hypothesis test with a significance level of 0.05 for the claim that all five categories are equally likely to be selected. So let's complete the table. So I have five outcomes or five categories. And when I actually counted those outcomes in the categories, I'll have the observed frequency. But then we have our expected frequency, what we were expecting to get. So what you do is you take your total outcomes here. We'll add up this entire column to get 67. And then you want to find out what does the expected frequency have to be in order to be the same for every category. So you take those 67 outcomes and you split them up evenly among five categories. And it looks like you get an expected frequency of 13.4. So 13.4 would be your expected frequency for all the categories. And then once again, that's because it said in the question that the claim was that all five categories are equally likely to be selected. So they're all equal. Now to calculate the test statistic degrees of freedom and P value, we go to Google Sheets. Google Sheets for goodness of fit. You are going to go to the Chi Square tab. You're going to choose goodness of fit from the drop down menu. And then you will type in your rows and columns of data. So column D, type your categories, your column categories. The labels for each row A, B, C, D and E. And then do your column headings you have observed. You have expected you don't actually have to write out the full title if you don't want to. So observe was the following numbers 22, 17, 5, 13, 10. Expected frequency would be all 13.4. Now, give your Google Sheets some time to calculate. Takes a little while to get the test statistic. Chi Square is your test statistic. The reason why is because anytime you do a goodness of fit test, it uses the Chi Square distribution. So it looks like the Chi Square test statistic is going to be about to three decimal places, 12.627 degrees of freedom or four. And the P value is about 0.0132.0132. So let's jot down that information. So my Chi squared, that's what a Chi squared symbol looks like. Test statistic is going to be 12.627. Degrees of freedom is going to be four. And then your P value is 0.0132. Now, to come to a conclusion about our claim, we need to compare the P value to alpha. So let's compare our P value to alpha. And the goodness of fit test, your null hypothesis is always that the frequency counts agree with the claim distribution. And then the alternative hypothesis is frequency counts do not agree with the claim distribution. Since the P value is less than alpha, we do reject the null hypothesis. Remember the null hypothesis was our claim here. We claim that the frequencies occurred all with the same frequency in each category. So we rejected the null hypothesis. It's rejected. It's gone. We need to write a conclusion statement about our claim. Well, we rejected our claim. So we say there is sufficient evidence to warrant rejection of the claim that all five categories are equally likely to be selected. And that's how you conduct a goodness of fit test.