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(20 points} The number of men and women among prolessors tWO academic arcas (Science Kumanities) Irom slmple random sample of sm colleges were counted,and the resul...

Question

(20 points} The number of men and women among prolessors tWO academic arcas (Science Kumanities) Irom slmple random sample of sm colleges were counted,and the resulls are shown (he table belav Sclonce Humanitles Mien Women Use Ine 0,01 level of significance detonino whether = not the relatiansnip between sex and academic area statistically signliicant;numbor(c) Is the relallonship betwoen sex and acudemic ure4 s1ulis(ICAlly aignllIc4nt?ANo YosMogic

(20 points} The number of men and women among prolessors tWO academic arcas (Science Kumanities) Irom slmple random sample of sm colleges were counted,and the resulls are shown (he table belav Sclonce Humanitles Mien Women Use Ine 0,01 level of significance detonino whether = not the relatiansnip between sex and academic area statistically signliicant; numbor (c) Is the relallonship betwoen sex and acudemic ure4 s1ulis(ICAlly aignllIc4nt? ANo Yos Mogic



Answers

Test the given claim. Listed below are student evaluation scores of female professors and male professors from Data Set 17 "Course Evaluations" in Appendix B. Use a 0.05 significance level to test the claim that female professors and male professors have evaluation scores with the same variation. $$\begin{array}{l|l|l|l|l|l|l|l|l|l|l} \hline \text { Female } & 4.4 & 3.4 & 4.8 & 2.9 & 4.4 & 4.9 & 3.5 & 3.7 & 3.4 & 4.8 \\ \hline \text { Males } & 4.0 & 3.6 & 4.1 & 4.1 & 3.5 & 4.6 & 4.0 & 4.3 & 4.5 & 4.3 \\ \hline \end{array}$$

For the first problem, we want to find the conditional probability that a person is male and is a secondary, educate their. So what that is going to look like is this this conditional probability of mainland secondary education. So we're going to have an intersection of M. And S. Over P. M. S. So like Tony six. All we do in problems like this is just cancel out our denominators and we get 28/70. We can simplify this 14, 30 nights. And so for the second problem, we will find the person, the person does not have a college sugary given that that person is also female. So what we're going to do for this problem is we're going to find the conditional probability of Nazi given the person is female. And so what that is going to be 1 -1 the conditional probability of a person being having a college degree and being female. So that's gonna be one minus 17 over 200 over 1, 12 over 200. We're going again, cancel out the two hundreds. And I'm gonna show you a little trick This is going to really end up being 1 -1 17 12, 112's and when and see what we did here is you see, we just took out that we combined 17 112. And when we make this, we're going to bring it down, Will have 112 over 112 to signify our whole number. Mine is 1700 and 12 and you get 95 Over 112.

So let's start by looking at the definition of probability. So what is the probability? Often effect. So probability. Often event equals number. Oh, favorable outcomes. These are the outcomes that be want divided by the possible number off all outcomes or it would be the total number of possible outcomes. So if we could start working with this basic definition of probability. So the question that we have to answer is what is the probability off employed with degree. So this is D probability that we are trying to figure out Okay, so, uh, remember that the total number of people surveyed was eight hundred. So this is the total number off outcomes, So total possible outcomes if you choose a person at random. There are eight hundred people to choose from now. The favorable outcomes are people who are employed and they have a degree. So we have one hundred and eighty eight females who are employed and they have a degree. And then we also have one hundred and seventy seven. So, males, this one it where did this come from? So this is females implied females with Diggory and the one seventy seven These are employed meals with a degree so adding those two, we give me the total number of possible of favorable outcomes and this comes out to be equal to three hundred and sixty five over eight hundred, which simplifies too seventy three over one hundred and sixty. So the correct answer option for this question is option is

Yeah. Now we have been given a few examples and we want to identify whether the data sets our population or sample. So grading point averages of all the students of the college, all the students of the college. This forms of population, Right? This forms a population. Okay then the gps of randomly selected group of students on a college campus. Now we are not selecting all the students were randomly selecting students. So this is going to perform our samples. Great. Okay Then the ages of nine Supreme Court justices of the United States on January one, Now, we are considering all nine. So this is basically the population you will say, How can only nine of them from the population will nine is the number of, you know, Supreme Court justices that you have in the entire country. So this is all of them. So this is our population. But the the gender of every second customer. Every second customer. So this becomes a sample. We're not considering everyone. right? So this becomes a sample. Then the length of atlantic crocus caught on lens of atlantic progress caught on a fishing trip to the beach. Now, this is again going to be sample because you're just going to consider the ones that you have caught, right? Not every single one. So this is again a sample. These are my answers.

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.


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