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NBC News/Wall Street Journal Poll conducted by Hart Research Associates (D) and Public Opinion Strategies (R) Aug 10-14, 2019_ N=1,000 adults nationwide Margin of ...

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NBC News/Wall Street Journal Poll conducted by Hart Research Associates (D) and Public Opinion Strategies (R) Aug 10-14, 2019_ N=1,000 adults nationwide Margin of error 3.1."Do you feel confident or not confident that life for our children'$ generation will be better than it has been for us?"NotConfidentconfidentUnsure8/10-14/19 8/5-9/17 7/30 8/3/14 5/16-20/12 8/26-/30/10 12/11-14/09 6/12-15/09 9/19-22/08 12/14-17/07 1/07 7/06 12/01 9/93 12/92583035 30 33 495662

NBC News/Wall Street Journal Poll conducted by Hart Research Associates (D) and Public Opinion Strategies (R) Aug 10-14, 2019_ N=1,000 adults nationwide Margin of error 3.1. "Do you feel confident or not confident that life for our children'$ generation will be better than it has been for us?" Not Confident confident Unsure 8/10-14/19 8/5-9/17 7/30 8/3/14 5/16-20/12 8/26-/30/10 12/11-14/09 6/12-15/09 9/19-22/08 12/14-17/07 1/07 7/06 12/01 9/93 12/92 58 30 35 30 33 49 56 62



Answers

Wrong direction An Ipsos/Reuters poll of 2214 U.S. adults voters in April and May 2017 asked a standard polling question of whether the United States was headed in the "Right Direction" or was on the "Wrong Track." $54 \%$ said that things are on the wrong track vs. $33 \%$ who said "right direction." a. Calculate the margin of error for the proportion of all adult U.S. adults who think things are on the wrong track for $90 \%$ confidence. b. Explain in a simple sentence what your margin of error means.

And question number 40. That given is X equal to number of success is equal to 256 and then is equal to sack a size equal to 256 plus 769 equal to 1000 and 25 sports See confidence interval equal to 90% equal to operate 90 for step one state. We are interested interested in estimating the population proportion p eg the 99 confidence living 99% Confidence Kevin which be is proportion off others who are satisfying with how things are going for Step two. The plan we planning on chemical ish in a one sample that interval for a population proportion being for random condition conditions. Satisfied? Okay, satisfied because the sample off 1025 others are are less than 10 person. Yeah, because the others come from a random sound of for two persons condition. Satisfied because the sample off 1000 and 25 others are less done. 10 person off the entire population off others flush counts condition He's satisfied because and by p are equal for number. Oh successes people to 2000 256 bigger than or equal 10. And and boy, he minus B one minus be equal to number off trailers equal to 769 bigger than or equal 10. We know that all three conditions are satisfied. We're going to step three. Do sense. All conditions are satisfied. We can deter mined that. The one sample is that interval for proportion resemble profusion is the number of successes divided by the sum. Besides so something proportion which is equal to the number of successes divided by synthesize equal to 256 over. 256 plus 700 and 69 go to 256 over 1000 and 25 will approximately equal to oh boy 2000 and 498 for confidence living one minus Alfa equal 90 person equal toe open 90 To deter Mined that for also over to equal to that for opened a while using table a look up all 0.5 is the people is that the score is then the found dead school was opposite time so that Alfa over to equal to that a 0.45 equal to 1.6 145. The margin of error is then equal to this for us over to boy square, but with or beef boy one minus B ever m equal to 1.645 boys square root for opening to for lying eight by one minus opened 498 over 1000 and 25 with approximately equal to offering it all 222. The confidence interval is then will be four point 22,000 and 276 equal to 4.204 100 2000 and 400 98 minus all 0.0, 222 people to B minus e this with them, He with them. Mhm, yes. Mhm Equal toe offering 24 98 plus opened or 2200 and 22 equal toe over. In 2000 and 720 Force. The four conclude we are 90% confident that the two proportion off others who are satisfied with how things are going is between oh, plane 2000 and 276 um, on opening 207. 2000 and 720 or between 22.76 person and 27.20 person. And that the final answer for that question. Thank you.

All right. We want to construct a 95 confidence interval about the population proportion P for the following survey results in a survey of 20 to 30 1270 to say yes. So in order to construct this confidence interval, remember that for a population proportion. The intervals defined as P between P hot minus E and P hat plus E. P hat is our test statistic given from our survey proportion are over and equals 12 72. Over 20 to 30 equals 300.57 E. In our margin of error, it is equal to the critical Z score associated with the confidence level times square root of P hat times Q hat over. And where Q hat is one minus P hat If we use a Z table or a normal distribution C. D. S, we can obtain Z score for 95% confidence. 1.96 stuff we've learned to hire 1.96 times square root .57 10.43 over 20- 34.0- one. So we have a confidence interval of 95%.549 is less than P, less than .591. So we are 95 confident this interval containing you.

But this problem refers to a survey of 1000 adults, and it was concluded with 95% confidence that from 49% to 55% of Americans believe that big time college sports programs corrupt the process of your higher education institutions. So and was 1000 and we were given a confidence interval at the 95% confidence level of 0.49 up 2.55 So if we think of that in terms of a number line, the low end is 49% the high end is 55% and part A is asking you to calculate the point estimate and the point estimate is identified with the variable p prime. And every time you do a confidence interval, the point estimate is found right in the middle of your confidence interval. So in order to find P prime, we could average the two endpoints of our confidence interval. So we'll take 0.49 plus 0.55 and we'll divide by two. And in doing so, you're going to get a point estimate off 52% or 520.52 The other part of this problem or part A asked you to find the error bound, and the error bound of the proportion is going to be that wiggle room. So it's the distance from the center to each end point of the confidence interval so we can get that by taking the high end of the confidence interval minus the point estimate which gets you three. Or you can go from the point estimate 0.0.52 and subtract the low end. And either way, we get an error bound of 0.3 In part B of this problem, it's asking, can we, with this 95% confidence, conclude that more than half of all American adults believe this? And the answer is no. We cannot conclude that more than half, and the reason being would be because our confidence interval spans from 49% up to 55%. So that means your true proportion can be anywhere in there in that interval. And since the interval goes as low as 0.49 we might be here, which could be less than half so. Therefore, no. We cannot conclude that more than half of all American adults believe this based on this confidence interval as we go into part, C. Parsi is asking you to construct a 75% confidence interval. So we're going to use the P prime that we found in part A and that was 0.52 And we're going to use the fact that we surveyed 1000 people and we need to find the confidence interval well. In order to find the confidence interval, we will need to find the error bound of that proportion, using the Formula Z of Alfa over to multiplied by the square root of P prime times Q prime over N. And in order to calculate the Z score associated with this elf over to, we will need to draw our bell shaped curve, which then puts 75% confidence into center. And our Alfa is the part of the curve that is not accounted for in that confidence interval. So there's 25% of the curve still unaccounted for, and because the bell shaped curve is symmetric, each tale will have half of that or 0.1 to 5. So in each tale we can put a 0.1 to 5 or 12.5%. And then the Z score associated with this left boundary can be found by doing. You're in verse norm on your graphing calculator. And when you use inverse norm, it asks you for three parameters. It asks you for the area in the left tail, which is 1.1 to 5. It asks you for the mean of the standard normal curve. And the standard normal curve has the mean of zero and the standard deviation of the standard normal curve, which is one. So I'm going to bring in my graphing calculator and to access inverse norm, you're gonna hit the second button, the variables button and number three, we're gonna type in the area that's in the left tail, followed by the mean, followed by the standard deviation of the standard normal curve. And we're getting a Z score of approximately negative 1.15 So that negative 1.15 is the Z score associated with the left boundary of the confidence interval. And because of the symmetric nature of the bell, the right boundary is going to be positive 1.15 So, in order to find the error bound of that proportion, we're just going to use 1.15 as RZ and the P prime was 0.52 We're going to multiply that by Q Prime and P Prime and Q Prime must add up to one so Q Prime would be 10.48 and R N was 1000. So our 75% confidence interval error bound is going to be 750.182 So we're not finished yet. We still have to generate our confidence interval. So to generate our confidence interval at the 75% confidence level, we're going to take the point estimate and we're going to subtract the error and we're going to take the point estimate and we're going to add the error. So our estimate was five to so we will subtract 0182 and then we'll take 0.52 and we'll add 0182 So for part C, our confidence interval will be 0.5018 up 2.5382 So the final part of this question is part D. Can we, with 75% confidence, conclude that all American adults believe this, and the answer to that part is yes. We can conclude with 75% confidence that at least half of all Americans believe that big time sports programs corrupt the process off the higher education system. And the reason being would be. Here's our point estimate of 0.5 two, but this time our interval on Lee goes down as low as point 5018 And if the true proportion is found in here, it's always above one half or 10.5. So, yes, we can conclude with 75% confidence that all American adults believe that.

Ms. Problem says that there was a Gallup poll asking whether or not people experience stress for a lot of someday, and 40% reported that they did feel stress. So how is this poll conducted? Well, they say results are based off of a telephone interviews. Ah, with some number of participants, with 170,000 545 adults 18 and older conducted in January to June in 2009. So what is the population? Well, that's like the entire population of potential people that could have been in this survey. So we presume, based off of what Gallup says, that they're interested in a national adults. So American adults aged 18 and older. Now what is the actual sample will? That's the people who participated in this study, which were these ah 178,545 participants. Party asks to explain how under coverage could lead to bias in this survey. Well, there's lots of potential places for bias and polls and surveys, but in this particular one, since it's a, uh, a telephone survey, the under coverage bias could be caused by the fact that some people that the only people who are responding or the people who have a telephone so people who own a telephone might have opinion, different opinions and those who don't. And of course, you know you think about the people who actually picked up the telephone to answer the poll. What does that say about you know, these people, these people who were able to answer the telephone? Why are a different population than just in general population of the U. S.


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