QUESTIONExhibit 6 [ Louis Harris Poll used survey of 1008 adults learn about how people feel about the economy- Responses vere as follows: 595 adults 332 adults 81 ...

The Financial Times/Harris Poll is a monthly online poll of adults from six countries in Europe and the United States. A January poll included 1015 adults in the United States. One of the questions asked was, "How would you rate the Federal Bank in handling the credit problems in the financial markets?" Possible responses were Excellent, Good, Fair, Bad, and Terrible (Harris Interactive website, January $2008 ) .$
a. What was the sample size for this survey?
b. Are the data categorical or quantitative?
c. Would it make more sense to use averages or percentages as a summary of the data for this question?
d. Of the respondents in the United States, 10$\%$ said the Federal Bank is doing a good
job. How many individuals provided this response?

So the Harris poll pulled 25 13, 2,513 adults. Of which 76% said that they like paper money. So to find out that exact amount, we'll just multiply of our sample size and the proportion or percentage and roll gets 1909 with a remainder of .88. Now we can't have 88% of a person. That would be silly. So for part B we can't have that much Now. See says Okay, what do we rounded up to? Well, 1909.88 is closer to 1910 than it is 1909. So rounded up to exactly 1000 and 10 people that liked paper cash. And then Couple of respondents said that they preferred prefer the currency in the form of a coin that's 327 of them. So our probability or our percentage of people that like that, it's going to be 327 Out of the 2513. And now that will get us 0.13 012 or 13. Yeah.

All right, this question asks us about a population proportion of 0.56 which is the proportion of Americans who have balanced their checkbook at least once a month. So Part A wants us to graph the sampling distribution for the P hat of a sample of 400. So since we have a large sample of 400 are large counts, condition is satisfied, so we know that this is going to be normal so we can just draw a bell curve here with a mean at the population proportion and a standard error of square root P times one minus p all over the sample size. So, no, it wants the probability that a sample of 400 is within point or two, which is the same thing as saying the probability that we get a P hat between 0.54 and 0.58 and to do this, we'll use normal CDF of our lower bound 0.54 are upper bound 0.5 with our mean 0.56 and then our standard error because we're working with a sample, not just one. Their sample of 400 and this works out to be 0.5 a zero No, it wants us to find the probability that we're within 0.4 of the mean, which is the same thing, is asking What's the probability that we get a P hat between 0.52 and 0.60 which again will use normal CDF for with our lower bound of 0.52 our upper bound of 0.60 our mean of 0.56 and our standard error of 0.56 times 0.44 all over the square root of our sample size, and this turns out to be point a 930

All right, So we're looking at 2009 survey about American adults. Opinions on Social Security. They found that of. Here we go. Come on. There we go. A sample of 2000 American adults, 1760. Security was a major economic concern. So part A, you want to find a point estimate for a proportion? That's gonna be just 1760 divided by 2000 which is 0.8. Eat. All right. Her to watch this defined and 90% confidence margin of error. All right, so rz statistic at 90% critical value of one point 645 So a margin of error for a proportion is going to be 1.645 times point estimate of our proportion 0.0.88 times the complement of its or one might is 10.88 which is ah, 0.12 divided by the size of our sample. And it compute this out, you get zero point 01 to 0 as a margin of error. All right, Now, for part C, you want a 90% confidence interval, so that's just going to be 0.88 plus or minus. Our margin of error. 0.1 to 0, which is 0.8680 to 0.8 Stein 20 There's that. All right, party. We want to find a 95% confidence interval with the same data. So a point estimate is still gonna be the same. 4.88 We find a margin now for a margin. Vera, we know that are critical value 5%. 1.96 So we have that our march of air is gonna be 1.96 times. The radical itself is not going to change, so we can just rewrite that. Ah, sorry s o So 1.86 and then times 0.88 times 0.12 divided by 2000 I realized I'm drawing my radical signs a little small. So if that noise you, I apologize. Uh, just gonna quickly x that that would go Niedere. Anyway, this margin of error turns out to be zero point 01 or two, which makes sense that it's larger than this one. Because as we get more confidence, we widen our confidence interval So we 1.88 plus or minus 0.142 which is the interval? 0.8658 to 0.8942 and there you have it.

All right. We want to answer the following question. In a trial with an equal to 10,011 that is 1000 and 11 observations, we observe a certain event 435 times from this information. We want to complete a through D which require us to construct two confidence intervals for the population. Should be and analyze first. We need to check the requirements for constructing any confidence interval of this sort. This gives the point estimate periodicals are around one point point five for this. We need to check the requirements of the bottom NPR one minus p. How critical the 10 sentences to 50. It is greater than 10 and requirements are met. That's proceeding out of the confidence interval. Our first interval has significant 92% confidence intervals. P hat plus or minus E. Where E is the Z score times Rupee one minus P over N for alfa is 1.92 and 0.1 point +751 Thus E is 7510.0 to 7 in the confidence intervals 70.4232 point +477 For this, we conclude that were 92% confident the population proportion falls in these bounds for our next interval we simply have to change the score. So for alpha equals 920.96 Z is 2.54 Therefore es 0.32 and the confidence interval that we are 96% confident now that the population proportion falls into is 960.4, we need to point for you to Finally, in part two, we answer, how does increasing the confidence from BBC affect the length of confidence interval? Clearly it increases the length of the confidence.