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Separate random samples of male and female high school students which award they would prefer to win: an were asked Academy Olympic gold medal. The results award, a...

Question

Separate random samples of male and female high school students which award they would prefer to win: an were asked Academy Olympic gold medal. The results award, a Nobel Prize, or an are summarized in the table below:Academy Nobel Olympic Totall Male 20 76 73 169 Female 11 79 109 199 Total 31 155 182 368Use PMACC (clearly label each step on your paper) to determine if there is significant evidence of a difference in the distribution of preferred awaed among all bigh school students. Use a signi

Separate random samples of male and female high school students which award they would prefer to win: an were asked Academy Olympic gold medal. The results award, a Nobel Prize, or an are summarized in the table below: Academy Nobel Olympic Totall Male 20 76 73 169 Female 11 79 109 199 Total 31 155 182 368 Use PMACC (clearly label each step on your paper) to determine if there is significant evidence of a difference in the distribution of preferred awaed among all bigh school students. Use a significance level of 0.05. Round aicvaluaru arone class_



Answers

Study habits The academic motivation and study habits of female students as a group are better than those of males. The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures these factors. The distribution of SSHA scores among male students has mean 105 and standard deviation $35 .$ You select a single male student and a single female student at random and give them the SSHA test.

(a) Explain why it is reasonable to assume that the scores of the two students are independent.
(b) What are the expected value and standard deviation of the difference (female minus male) between their scores?
(c) From the information given, can you find the probability that the woman chosen scores higher
than the man? If so, find this probability. If not, explain why you cannot.

A problem. Number 52 and a of the students where selected that trend them and randomly Ah, selected signals. And me, I assume we have in revenge Bent course it's was his explanation or point a six point B Ah, for fun. Be, um we know that the new off if it's 1 20 there's some will be the agent Ah, stand on the vida off Rash is 28 and then you, uh um ah, the new open is well working with five. Still, division is a 30 crime. Okay, So if x and y are independent so the new of X minus Y is able to the new vax minors, um, you'll want so badly Ah ah If, uh my and it's me old, uh, we're very rooms in capital letter. So it would be, ah, mean or graph minus the mean man. So this is 1 20 minus 25 which is, I mean volumes minus and is equal to, um, variance or Istanbul. Ah, these in Rex V squared? Uh, yes, it's under the ignition or end a square. This is a property and it's a property. If x and Y are independent s so we can say so it squared plus, uh, 35 Where? Certain paper toe percent of the end. But mine eso we can say that somebody division f my understand is equal to the square root there somewhere on nine, which is equal to 44 point 8 to 1 that one night. And this is the answer for for me. Ah, question. See? And you can see that not we'll see. Approved. Burkle finds on the probability. Uh ah. Do we really think make a wish? Way? Doughnuts? No, at the distribution. Oh, the scores, for example. A normal uniform. Well, we don't know the distribution. Um, we don't know the distribution for for the scores. What is its signature is not possible to find in the Caribbean. Obviously, the question for 3 50 to see.

All right guys, so for this one, um First we need to start by identifying or null and alternative hypotheses are no hypothesis is that there is the same variants being male and female professors and alternative hypothesis that there's there's a difference between male and female professors when it comes to variation variants, I should say. Um So okay, so with that um with that, what the next thing we need to do is we need to go ahead and identify our f statistic. Um and that is going to be found by opening a google sheet, at least in my case I opened google sheet and I want to hand his input all the data from the table. Okay. In order to find our F test statistic first and put in the day to the next thing I did as I found the variance. Okay, it's by the V A R equals V A R in a cell and I highlighted the data. I wanted to find the variance in and I enter and then the variance for the second one was right there. I hit enter. Awesome. Okay, cool. So it looks like the variance for the few professors is much higher. So it looks like our female professors. Well BS one sq and our male friends will be S two squared because s one square it has a higher variance. So to find the F. Test statistic, I just need to divide the larger variants by the smaller variance and there it is 4.175 Very large F statistic right there. All right. So the next thing I need to do is this I need to calculate the p value in order to calculate the P value with an F statistic. You do need to have the F statistic, but we also need to find degrees of freedom for the data. So here's what I'm gonna do that in google sheets. Of course I could count manually. But if another way to do it is actually just do this do equals count and it will actually count all this stuff for you. Okay. But degrees of freedom isn't a direct count, degrees, freedom is account minus one. And so that's what I'm going to put and that's gonna be nine and this should be the same. But let's just check just in case count of that minus one and there we go. Nine. Okay. So for my p value, what I'm gonna do is I'm going to start an F. Distribution also known as F. Dist and open parentheses and idea input. Three values the first value, the F statistic and the second two values are the degrees of freedom. Close my parentheses do that and we get a fairly small, we get a very small p value right there. However, what we do need to do is this we're not quite done yet because this is a one tailed P value. What does that mean? That means this P value of work. If that is a less than or greater than symbol, It's a non equal simple, not equal, simple is a two. Uh is a two way distribution. Okay? Which means it's going to be twice as large as a one way, which means in order to get the correct value, I need to take this and multiply or asterisk in google sheets by two. And that is my p value right there. So this p value, they asked us to use 0.5 significance level. Is that less than 0.5 barely. But yes, that is less than 0.5 So there is sufficient evidence to reject the null hypothesis. So there is sufficient evidence to reject the null hypothesis.

So let d be the difference between the male rating for attractive ists and the female in that order. You always want to label that And we have 12 pieces of data. Uh huh. And we find that the mean of those numbers becomes negative .2083 with the three repeating. And the standard deviation of those differences comes out to be 2.168 level. Call it six. And we will be assuming That the main difference is equal to zero and then alternately mean difference is not equal to zero. So it's like we don't know which direction that difference is going to take place. So we're just going to find out if it's different. And so we have in our picture that the difference is zero is what we're assuming We're actually getting a negative difference of about negative .2 or the D dehap. Excuse me. D. Bar. And since we're doing a two tailed tests this is just as likely as this as a positive point to. So these two areas combined will be R. P. Value. So we want to find what's the likelihood of sampling from a distribution that truly is centered at zero and getting the mean With 11° of freedom. Since we have sample size of 12 Being less than or equal to negative 2.0, excuse me, .2083 repeating. And we want to double that because we want to find both of these tales for our two tail test. So now we'll change that into our test statistic Which will be a. t. value with 11° of freedom. I guess we didn't need to write that there and we take what we got minus what we're assuming they mean to be divided by the standard deviation over the square root of an Yeah. And when we do that we find out that are test statistic comes out to be Very close to zero, negative .33-8, which means in my picture this value should have been way up here in way up here so we can see that that p value was actually going to be very, very large. And when we get that value, make sure you double when you use T C D. F. Or use your software to find that value. We get that. The p value comes out to be a Close to 75%,, Which is definitely not less than 5%, which was the significance level that we were going to use. So we fail to find evidence to reject them all. So it does appear as though that mean difference between the male and the female really does seem to be approximately zero. So that overall the average is basically a zero. Where they kind of a wash, they don't appear to be different.

The farm is a solution for number 15. And this looks at private versus public school teachers to see if they have NBC licenses. And for private out of 80.175. So that they hold this particular license. And for public out of the 520 15% that they hold this license. So the point estimate for P one minus P. Two. It's simply just the statistics behind that which is P one minus P two hat. And that's actually given to us. So the P hats are over here. So let's just assume that the first is private and the second is public. So 20.175 minus 0.15. And that's 0.25. Okay, so that's the point estimate Now we find the 90% confidence interval. And if we go to stat and air over two tests and then go over to the b option to prophecy until we can type in our data. Oh, I forgot to show you this. So the ex and the X one X two. We actually need to find that. Um So the way you find that I'll do it up here. So X one, it's just the end the sample size times the P hat. So if we take 80 times 800.175, you should get 14. And then If you take 520 times .15, you should get 78. So those are your favorable the number favorable. So they give us the proportion here and we needed the number here for to use the calculator. So 14 out of the 80 should give you that 800.175 and then 78 out of 5 20 should give you that 200.15 and we want to be 90% confidence 2.9 and then we calculate and this top part here, the negative 0.5 and the positive 0.10. Those are our um boundaries for the confidence and also negative zero point I'll go ahead and keep the same 04 95 all the way up to 099. I'm sorry, that's not right. Zero point 099 47. Okay. So those are yeah Boundaries for the 90% confidence interval. Okay. And then the third parts apart C we need to do the uh hypothesis tests at the 10% level of significance where the null hypothesis is that there is no difference. And the alternative is that P one is less than P two um or in other words, you know what, that's not going to make any sense. It should be. P one is greater than P two, shouldn't it? Since those proportions are higher. So greater than. Okay, so those are basically we're gonna do here. So we need a Z value or test statistic and then the p value and we're going to compare that to our alpha value that's gonna tell us whether to reject or not reject. Okay, so I can go back to the calculator and if I go to stat tests and then I can do the two proportion Z. Test. Okay And um here you have you know all this stuff here and then. No I'm second guessing myself. Is it less than or is it greater than? Yeah it should be greater than right because yeah okay so greater than so I'm going to move this over here and then I calculate And my test statistic is .5777. And my p value is .282. Okay so .282. Okay which is greater than alpha? And my test statistic is 0.5777. Okay so the p value since it's greater than alpha I'm gonna fail to reject the H. Not so I'm failing to reject h not meaning I'm rejecting I'm failing to reject the statement that these two are the same. So the proportions are roughly equal um private versus public. NBC teachers. And then the last part of this was to find AP. Value already did. So the P values this .282


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