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According to a survey, 10% of americans are afraid to fly.Suppose 1,170 americans are sampledA. Is it safe to assume n<= 0.05B verify np(1-p)>= 10suppose we a...

Question

According to a survey, 10% of americans are afraid to fly.Suppose 1,170 americans are sampledA. Is it safe to assume n<= 0.05B verify np(1-p)>= 10suppose we are interested in the probability percentage that 150or more americans in the survey are afraid to flyb. draw a figure by shading the region that corresponds to thescenario given. the z- score is z = 3.2c. what is the probability percentage that 150 or more americansin the survey are afraid to fly? round to the percent to twodecimal pl

according to a survey, 10% of americans are afraid to fly. Suppose 1,170 americans are sampled A. Is it safe to assume n<= 0.05 B verify np(1-p)>= 10 suppose we are interested in the probability percentage that 150 or more americans in the survey are afraid to fly b. draw a figure by shading the region that corresponds to the scenario given. the z- score is z = 3.2 c. what is the probability percentage that 150 or more americans in the survey are afraid to fly? round to the percent to two decimal places. D. interpret the probability found in part c. in context of Americans that afraid to fly.



Answers

Use the figure, which shows the results of a survey in which 1044 adults from the United States, 871 adults from Great Britain, 1097 adults from France, and 1003 adults from Spain were asked whether they consider air travel to be safe. (IMAGE CANNOT COPY) Construct a $99 \%$ confidence interval for the population proportion of adults who consider air travel to be safe for (a) the United States. (b) Great Britain. (c) France. (d) Spain.

Where is the formula for N? When pick up is unknown, which is the first case, right? If I look at the first question, nothing is known about the percentage of passengers who prefer aisle seats. So in this case, my pickup is not known. So the formula is in is equal to Z Alfa by two square into 0.25 upon e squared. What is the value of fee? I want this to be within 2.5% points 2.5 minutes 0.25 right, 215 means zero point. Yeah. Zito to fight. Okay, now what is my confidence level? 95%. So my Alfa by two will be 0.25 So my Z off Alfa by two is 1.96 So my Z off Alfa by two is equal to 1.96 Now I have all the values. I just substitute them in this formula. And what I get is my end in this case. Turns out to be 1537 1537 Now moving on the part B now in part B, I have my peak apus. 0.38 I have my P cap as 0.38 Hence my cue cap will become 0.6. Do so what is the formula in this case and is equal to Z Alfa by two whole square Speak up que gap upon e squared. I know all of the values. I substitute them. And the value that I get is for 14 49 right, 14 49. This is my minimum sample size in case B and these would be my answers.

We have n equals 25 values, transformers, symmetric, mound shaped distribution sample mean is equal to 10 and the sample standard deviation is equal to two. Using a significant level of alpha equals 20.5 conducted to tail test of new equals 9.5 on the stand for the population. Me first, you have to answer A. Is it appropriate to use a distribution for hypothesis test for this? Yes. It's the distribution of symmetric and mount shape so we can use a student's T distribution. Note that the degrees of freedom is equal to end minus one is equal to 24 in this case, next one of the hypotheses, the hypotheses are h not mu equals 9.5. An alternative hypothesis. You does not equal 9.5. Next let's compute t remember the formula for tea, which is given here. This computes out the T value 1.25 Next let's compute the p p interval using a T interval. We see that P falls between 0.2 and 0.25 for this T statistic. Next we deserve and whether or not we reject asian art. No, the entire P interval is greater than our significant level alpha. So we do not reject a chart, and we interpret this to mean that we lack evidence that suggest new. It's not equal to 9.5.

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.

Given the following information were asked to conduct hypothesis test to see whether a change occurred in the population proportion planning to travel by airplane over the 10 month period. So, um, I should say, 10 year period. But, um, what we have to first do is come up with the hypotheses are no hypothesis is going to be, um, that there is no significant difference so that the proper populations are the same. So it's a population of one is equal to report sorry proportions. The proportions of this unfortunate one is equal to the proportion of two. Um and then our alternative hypothesis is going to be that the two are not equal. And you can also write this as a difference of proportions. Soapy one minus P two is equal to zero for the no hypothesis, and p one minus P two is not equal to zero for the alternative. And now we have to come up with in port be Ah, the proportions, the sample proportions. So the P bar for, um, our first sample, which is 2003 is equal to the proportion of or the number of people expecting to travel by airplane over the total number of adults sampled. So that would be 1 41 over 5 23 which is equal to 0.2696 and in percent form. That would be 27%. And our second sample proportion would be the number of adults sampled in 1993. Um, that would travel by airplane over the total number of adults sampled, which was 4 77 and we get a value of point 0.16 x 98 translates to a percent of 17. And now, using this information, we have to find a P value in order to test first thing you've been difference. So in order to find our P value for the first need to come up with a a pooled variant since we're working with with proportions. So our pool variance is going to be the proportion from sample one times the total number of people sampled. So, um, and one plus the proportion from to the second sample times the total number of people sampled in the second sample over the sum of the sample sizes. So for us, this is going to be, and this value right here is just the number of adults that answered that they would travel by airplane in the first sample. So that is equal to 1 41 That's 1 41 right 1 41 plus 81 over 5 23 5 23 plus 4 77 This leads to a pool variance of 0.222 So our pool variants shredder here is able to 0.222 Now isn't using this pulled variance and our sample proportions? We can come up with a Z test statistic, so our Z score is equal to the first sample proportion, minus a second sample proportion divided by the square root of the pool variance times one minus the pool variants times one over the first sample size placed one over the second sample size, which is equal to, um, 0.2696 minus 0.1698 Divided by the square root of 0.222 times one minus 10.222 times one over 5 23 plus one over 4 77 And we get a Z score, uh, 3.79 So with this Z score of 3.79 if we draw our normal distribution, the depot zero in the middle we have is he equals 3.79 out here. And we are looking for the area that it to the right of Z equals 3.79 But because we have a two tailed hypothesis test is given by our hypotheses. It's not directional. Um, we have to find, uh, the the area of this curve that is less than negative 3.79 as well. So our P value was equal to the probability that Z is less than or equal to negative 3.79 or Z is greater than 3.79 which is just equal to two times the probability that Z is less than or equal to get a 3.79 And when we look at our ze table and come up with and, uh, if you value for just a probability for just this and multiplied by two, we get a P value of 0.4 And now we get to compare this against our Alpha of 0.1 Sorry. Let me just make sure this Ah Z score is right. So open up. Yeah. So, um, native three point Who could do this? Yes. So our, um, r Z score or rp value is 0.11 I don't know where that 0.4 came from 0.0 011 times two is equal to 2.22 And now this is our P value p equals 0.22 un. Compared to our alphabet, 0.1 equals 00 to 2 0.22 is less than 0.1 Therefore, we reject the no. And what does that mean? It means that there is sufficient evidence to support the claim that the proportions differ. Um, And now, um, you know, we have to look at reasons why this difference could occur. Um, it could be that, you know, um, one test one of the Poles was conducted in March. The other was in May. In may. You have school ending for colleges. So a bunch of people might be planning summer trips and things like that, whereas marches testing season for a lot of, you know, high schools and stuff. So they might be our families might not be traveling as much, So that's just


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