In question 2 to 6. We're going to be looking at the data on the political views off students who are classified as meal or female and as liberal, moderate and conservative. So in the first part of the question A. We're going to be looking at the traditional distribution off political views for me, for females. So we're going to focus mainly on the females and to focus on the female's. We'll have to walk out the rule percentages. So in this in each room, therefore there three different categories we have l liberal M moderates and see conservative. So for females, we have a total of 30 Feist females out off 77 females who considered themselves liberal. We will supply about 100% and we obtain 45 0.45%. For those who consider themselves moderate, we have 36 out of 77 times 100% which will be 46.75 cent. And the last category is for those who consider themselves conservative. We have six out of 77 times 100% and that gives us seven in 79%. So you'll notice that the majority off, the females consider themselves moderate, and the minority of the females considered themselves conservative by looking at those conditional distributions. The second part of the question be requires us to find the conditional distributions off political views for meals. So here we focus on males, and we're also going to now be looking at the root percentages. And we have three categories liberal moderates and conservatives. So there are a total of 115 mils and 50 off. Those mills consider themselves to be liberal, so you multiply the fraction by 100% and we obtain 43 point 48%. Second category. We have 44 meals that consider themselves moderate out of a total of 115 meals times 100% which gives us 38 0.26%. The last category is for the meal, so consider themselves conservative and we have 21 out of 115 mils multiplied by 100% and that equals 18 0.26%. So when you look at this values, you can tell that majority of the males consider themselves and minority of them consider themselves conservative now in Patsy were supposed to make a display that compares the two distributions. So in this case, we may need to use a side by side botch it to compare the two distributions. So that's okay. So here we have decided by side matchup, that compares the two distributions. So when you look at the bus, you can see there to buzz for each sex. For females, we have the blue bar, and for meals we have the they were inch bar. But D of the question requires us to tell whether the two variables are independent. So to determine whether these two variables are independent, we need to look at the proportions off males and females that considered themselves liberal, moderate and conservatives. Now, when we look at the fast bar for liberal, we find that the proportions off males and females are very similar. But we could just take this to oh bars to be of the same size. So the proportions for females and males who consider themselves to be liberal are very similar. But when you look at the second bar from those who consider themselves moderate, you find that more meals, actually more females considered themselves more merit than me. So, as you can see the fines is, there's a big difference here, indicating that more females considered themselves moderate than meal. And in the last category, you can see that the Taliban is for meals that more males consider themselves conservative than females. So that means that piece variables are not independent. Politics and sex are not independent.