 Hello, and welcome to the lesson on chi-squared tests. So in this lesson, the first part, we're gonna talk about chi-squared tests. And in this video, we're gonna talk about how we can develop a randomization procedure for those chi-squared tests. Now, the first step of any chi-squared test and for the majority of tests that we do in this course is defining our hypotheses. So here in Google Colab, I've already defined our hypotheses. We have our null hypothesis that each suit in this deck of cards that I have is set to 25% each. In other words, this is a fair deck. There's the same percentage of hearts as diamonds, as clubs, as spades. And then our alternative hypothesis is that one of those proportions is not as specified. It doesn't tell us which one, just that one of them is not. So before we get started, I'm gonna go ahead and draw some data from this deck of cards. So we'll go ahead and give it a shuffle. And essentially what I'm gonna do is fill in this table here, where I've got all zeros, and I'm counting how many diamonds, hearts, clubs, and spades we get. So I'm just gonna draw the top card from the deck until we've got about 20 cards drawn. And so the first card I drew was a spade. So I come in here, increase that to one, got another spade, a heart, a club, another heart, heart, club, another spade. So right now we haven't got a lot of diamonds. Here's a heart, another heart, finally a diamond. So we've got about 10 so far. So here's another diamond, diamond, club, diamond, diamond, heart, oh, I did that wrong. There should be a seven spade diamond. And I will go ahead and stop there. We've got just over 20 data points there. So now we're going to continue with the coding portion of the lecture. And so we now have our table. And this table is essentially, we're writing it in a dictionary. That's what these curly brackets mean. And then we're converting it to a data frame with the command PD data frame. And then we're gonna print the table. So I've already got my libraries added. So I'm just gonna go ahead and print this table, which is essentially giving us the count. So we've got six diamonds, seven hearts, three clubs, five spades. And our goal with this will be to determine whether or not these observed proportions are essentially close enough to a 25% proportion or whether they're not. And one sample isn't great in terms of our statistical analysis. And so what we're going to do is create that randomization procedure that we've done, a similar one to what we've done before, so that we can generate more samples.