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Minnesota had the highest tumout rate any state for the 2012 presidentia clccton Political unalysts wonder rurnout ruri Minnesota was higher Lhun tumout the urban J...

Question

Minnesota had the highest tumout rate any state for the 2012 presidentia clccton Political unalysts wonder rurnout ruri Minnesota was higher Lhun tumout the urban Jreas sample shows that 615 820 registercd voters from rural Minnesota volco the 2012 presidentia cicction while out or 575 registered voters from Umban Minnesota volcothe state Formulate and alternatlve hypotheses that can useo test whether reglstered vocers 2012 presidentia election- (Let P1 ulation proportion Vorers Minnesota uoted

Minnesota had the highest tumout rate any state for the 2012 presidentia clccton Political unalysts wonder rurnout ruri Minnesota was higher Lhun tumout the urban Jreas sample shows that 615 820 registercd voters from rural Minnesota volco the 2012 presidentia cicction while out or 575 registered voters from Umban Minnesota volco the state Formulate and alternatlve hypotheses that can useo test whether reglstered vocers 2012 presidentia election- (Let P1 ulation proportion Vorers Minnesota uoted voted in the 2012 election ) Mlnnesota were more Ilkely than reglstered voters Umdan Minnesota the 2012 election and population proportion of voters urbar Minnesota who Ho: P1 Ha: P1 Ho: Ha:P1 Ho: P1 Ka: P1 Ho: P1 Ha:P1 What the proportion sampled lstered vorens Minnesata chal Votco 2012 presidential# election? What portion samoieo registered voters Urban Hinnesota that voted the 2012 presidentia election? Ft ( 0.05_ test the polltical analysts" hypothesis. Calculate the test statistic_ (Round your answer decima places _ What the p-value? (Rouna UoMr answer t0 our decimal places:) D-value



Answers

Involve finding binomial probabilities, finding parameters, and determining whether values are significantly high or low by using the range rule of thumb and probabilities. In a presidential election, 611 randomly selected voters were surveyed, and 308 of them said that they voted for the winning candidate (based on data from ICR Survey Research Group). The actual percentage of votes for the winning candidate was $43 \%$. Assume that $43 \%$ of voters actually did vote for the winning candidate, and assume that 611 voters are randomly selected. a. Use the range rule of thumb to identify the limits separating values that are significantly low and those that are significantly high. Based on the results, is the 308 voters who said that they voted for the winner significantly high? b. Find the probability of exactly 308 voters who actually voted for the winner. c. Find the probability of 308 or more voters who actually voted for the winner. d. Which probability is relevant for determining whether the value of 308 voters is significantly high: the probability from part (b) or part (c)? Based on the relevant probability, is the result of 308 voters who said that they voted for the winner significantly high? e. What is an important observation about the survey results?

So the question asks when the in what years with the population of colorado be more than that of Minnesota. So I'm going to have 74 plus 4, +303 This has to be uh greater than 33. T plus 4 +98 So I just rearranged this 74 -33. T Equals 498, 8 -4, So I end up getting key equals five. Aid sex divided by one four, which equals 685, divide about 41 gives me 16.7. Let's round up down to 16. If T equals eight, is that 2008? Which was given in the question T equals 16 is going to be actually let's round that up Because I got 16.8. So yeah, T equals eight corresponds to 2008. So I just have to add 9 to this nine to both. Eight plus nine gives me 17 and this year correspondence in 2000 and 17. So beyond this year, the colorado population will be more than Minnesota, and the next question asks me to find the point of intersection algebraic lee. We can use this equation here. Well, actually, this was greater than right because it's in inequality So greater than 2017. And so I can use the same equation here to just find the point of intersection. So I get to, or 6 85 5 41 6 85 x 41. This gives me 16.707, so that's the point of intersection.

In this problem, we want to sample 250 voters from across three districts, which are our strata in this example to estimate the mean voter support on an issue. And this voter support is being measured on a scale from 0 to 10. So we want to make sure that we uh collect that. We randomly sample enough people from each of our three strata to make sure that everyone's proportionally represented. And because we have information about the sample standard deviations that were maybe gathered from previous data, uh in those districts, we can use this method of proportional sampling that takes into account the variation and responses. So first thing we need to do is determine the sample sizes for each district. So let's go ahead and calculate this these the number of individuals that I need to randomly sample from district one will be computed by taking n one times S one over and one times S one plus in two times S two plus n three times S three. And then we need to multiply that. Buy em and I realize now that I have an error in the expression that I had up here, this needs to be all times. Mm And when you're doing these problems, if you forget to multiply by m uh, it will be noticeable because you'll get a number that's between zero and one. Um, you should have a whole number that represents a sample size, so we would be able to tell pretty quickly if we had made a mistake. Okay, so N one number of people in district one is 1525. Number of people in the sample standard deviation from that district is 2.2. The sample size m that I want to have total across the district is 250 and then this is going to be divided by 15, 25 times 2.2 plus number of people in district Two times that sample standard deviation So 9, 17 times 1.4 plus 2890 times 3.3. Okay, and what you should get if you multiply that out in your numerator, you'll have see 83 or 838,750. And then in the denominator you should have 14,175 0.8. You might pause the video and do those calculations. This will give you 59 0.1677 If we stop at four decimal places and remember this is a sample size and we need to round to the nearest whole number. So we should sample 59 voters from district one. Okay, let's do the same process for district two. What we're going to have is in two times S two over. And because I've already calculated this denominator and it's not going to change, I'm going to just use the number that I calculated before 1 14,075 10.8. And this is times mm So we should have 917 taking this information from the table times 1.4 times 250 over that denominator. When you calculate this, you should get 22.6407 and rounding to the nearest whole number that will give us 23 voters from district two. And lastly, the number of people we need to sample from district three, that will be N three times S three over that denominator. That we've already calculated times the total sample size we want. So taking this information from the table will have 2890 times 3.3 mm is still 250 keep our denominator the same. And when you calculate that, you should get 1 68.1916 which will round to 168 voters. It's always a good idea to check, let's make sure that we did the calculations correctly and that this does indeed give us the total sample size that we want to have. So we'll add 59 from district one plus 23 from district two from 100 plus 168 from district three. And that will indeed give us 250 voters which is the value of em that we wanted. So everything checks out. You likely did our calculations correctly. So we'll get 59 voters from district one 23 from district two and 168 from district three. Then we're asked to actually estimate the mean voter support using some additional sample data. So what we want to do is estimate the true mean which we represent with the greek letter mu And we have a formula for that. We will need to have some sample mean information. So were given a sample mean from district one of 6.2 sample mean from district two of a 3.1 and a sample mean from district three of 8.5. And the formula that we are then going to use is N one over M times X. Bar one plus end to over M times X bar too plus and three over M times X bar three. Okay, so using our calculations from the first part, we have 59 over 250 times the sample mean given. Which is 6.2 plus 23 over 250 times the sample mean of 3.1 plus 168 over 250 times 8.5. And what you should get when you perform that calculation is approximately 7.4604 So if we wanted to round that to one decimal place, we could say that we're estimating the mean voter response across these districts to be 7.5 on a scale from 0 to 10.

And this video we will compute the sample size or the size of a random sample given three different areas. And using our knowledge of waited averages. So the formula we need to use is lower case and sub I. Equals capital N C B S A B. And then in the denominator you'll notice it's the capital end times the S. Plus N. S. Plus N. S. Times M. Where M. Is the sum of those Sample sizes. And in this particular example we want them to be 250. So what I'm going to do is I'm going to calculate the denominator because I'm going to have to use that each time and then I'll fill in the appropriate values in the numerator depending on whether I'm finding And a little lower case ends of one. Lower case ends up two or lower case ends up three. So I open up my calculator, clear out the screen and my denominator will be So that's capital and one times S one and two times S two and three times S. Three. So that's going to be my denominator. So I'm gonna take my eraser here And all of that will be replaced with 14175.8. And then we wanted em to be 250. Okay so now I just need to go through and substitute in the correct values. So the first numerator for an lower case n. one. Actually I'm gonna go ahead and put parentheses around it just so oops that's not parentheses. Just so you can see for clarification that that's the numerator, you don't really need them because the calculator will do order of operations. So there's the division and now I need to multiply that by 250. So it looks like my first value will be 59. Now I'm going to do this again But I'm going to use the N two values and I'm going to press second enter second enter because the calculator will call up that information again and I will just Type over 917 Times 1.4 and then select delete to delete that extra value. Press enter and multiply that by 250. So the next sample size will be rounding that up 23 And I will do the 3rd 1 the same way and multiply that By 250. So The third random samples should be of size 168. Now we're told that samples were taken and we do have averages from each and we're asked to find you or the mean for the entire population. So remember this is a weighted sample. So I need to go back to my sample size or a weighted average. I'm sorry. So I will do 59 times 6.2 Plus 23 times 3.1. So the sample size times the average sample size, times the average sample size times the average, So 1865.1. And I'm not done because remember it's the average. So I have to Take the sum and divide by the total. And in this case the total was 250. So I'll take the value that's in my calculator and divide that by 250. And that tells me that the average for the population Can be approximated with 7.46.

And so for this one, it says we want to pick from a registered voter who was eighteen to forty four years old in two thousand twelve. Which of the following is the closest to the probability that the registered voter was from the Midwest region? So first of all, we know that the baseline information is that the age group is from Fort eighteen to forty four. So here's eighteen and here's forty four. So we want to encompass both of these regions. Okay, so then that means that our new total is gonna be taking up taking out of this region. But then we want to know the possibility that it's from the from the Midwest region, which is this little box right here. So then we just have to take these two numbers and divided by the total for the eighteen to the forty four that's going to be three four five three plus eleven thousand two hundred thirty seven, divided by fourteen thousand seven hundred sixty six plus forty seven thousand eight hundred and ninety six. Then for the numerator, we get fourteen thousand six hundred ninety. For the denominator, we get fourteen popes, we get sixty two thousand six hundred and sixty two sin. If we divide that, we get about twenty three point four four percent, meaning that close ones probably be.


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