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-C7'Question HelpAfood safety guideline that the mercury fish should be below part per million (ppm): Listed below are the amounts of mercury (ppm) found tuna ...

Question

-C7'Question HelpAfood safety guideline that the mercury fish should be below part per million (ppm): Listed below are the amounts of mercury (ppm) found tuna sushi sampled al diflerent stores major cily: Construct 99% confidence interva the mean amount of mercury estimate of the population. Does appoar Ihat thero too much mercury in tuna sushi? 62*0 +S'0 0.10 0.97 33 0.57 0.93What is the confidence interval estimate of the population mean |?ppm < p <Ppm(Round to three decimal pl

-C7' Question Help Afood safety guideline that the mercury fish should be below part per million (ppm): Listed below are the amounts of mercury (ppm) found tuna sushi sampled al diflerent stores major cily: Construct 99% confidence interva the mean amount of mercury estimate of the population. Does appoar Ihat thero too much mercury in tuna sushi? 62*0 +S'0 0.10 0.97 33 0.57 0.93 What is the confidence interval estimate of the population mean |? ppm < p < Ppm (Round to three decimal places as needed )



Answers

Construct the confidence interval estimate of the mean. An FDA guideline is that the mercury in fish should be below 1 part per million (ppm). Listed below are the amounts of mercury (ppm) found in tuna sushi sampled at different stores in New York City. The study was sponsored by the New York Times, and the stores (in order) are D'Agostino, Eli's Manhattan, Fairway, Food Emporium, Gourmet Garage, Grace's Marketplace, and Whole Foods. Construct a $98 \%$ confidence interval estimate of the mean amount of mercury in the population. Does it appear that there is too much mercury in tuna sushi? $$\begin{array}{rrrrrrr} 0.56 & 0.75 & 0.10 & 0.95 & 1.25 & 0.54 & 0.88 \end{array}$$

So the first thing we'll do is find the mean of our values. Really taking a look at tuna from suppliers and the mercury content in there. So that's going to be all our values added up. And we're gonna divide it by seven. And what we end up getting is 0.72. Now for the median, we're going to arrange our values from at least the greatest. Since we have seven values are medium is going to be at the fourth place. Since that's going to be exactly in the middle between our 1st and 7th value there exactly three away. And that is going to be a 075 for our median. And then for the mode do we have a number that appears more than once? The answer's no. So our mode does not exist. Mhm. And finally, the mid range is going to be the sum between the smallest and largest value. So it's gonna be 0.1 plus 125, divide that by two. And what we get is 0.675. And what can we conclude about this is that Our store that has the 0.1 Mercury can't have gotten it from the same supplier since they have a lot lower amount. Since that their amount of mercury is a lot lower

Mhm. Now, over here, I wanna find to confidence intervals one is at 95% and the other one is at 99%. So at 95% my Alfa by two is 0.2 on. I want my e to be within 0.5. So let's say that the 0.5 for Alfa Beto A 0.25 my Z value is 1.96 which is what I've substituted over here. And I get my in value to be 1 20 point something. But since it cannot be a decimal value, I take it has one ready one. Now I want my confidence level to be 99% right. This is my first answer and is equal to 1 21. Now I want my confidence level of 99%. So my Alfa by two will become 0.5 I simply put in the values and I see that my end in this case is 20 night. That is in order to be more confident. My sample sizes also increased right. It only makes sense if I want to be most confident. I should have more number of samples. This makes sense. And even if we were to look it, look at it from the formula. My Z Alfa by two for 99% is going to have a higher value. And I want e to be the same as 0.5 So if my numerator increases, I want my denominator also be increased. And hence I can see that my end has also increased. And what is my end? My end has become from 1 21 it has become 209

In party. I want to find peak cap. Okay, So what will be peak app? My sample sizes. 5000 and 717 people returned. So I peek at is 717 upon 5000. This is my proportion. My sample proportion. If I use a calculator, this is going to be seven months. Seven divided by 5000 0.14340 point 1434 How do I calculate the margin of error? My margin of error is Z Alfa by two, multiplied by route over Big Gap Que cap by. And the end is the sample size, which is 5000. My Q is equal to my cue cap is going to be one minus p cap. So if I do that, I get 0.85660 point 8566 Okay, what is my Alfa By two? I want a 90% confidence. So my Alfa is 0.1 and my Alfa by two will be 0.50 point zero Fine. This is my Alfa by two. So if I use it calculated to calculate the critical value this is 1.6449 So I just put in the values 1.6449 multiplied by root off 0.1434 multiplied by 0.8566 upon 5000. So after using the calculator, let's just do that. This is going to be rude off 0.1434 multiplied by 0.85 66 divided by faith closing. So this is 0.49 fight. And if I multiply this with one point 6449 I get this a 0.815 This is this Value turns out to be 0.8150 point 00815 The third parties calculate the confidence interval. How do we do that? We know confidence. Interval is peak ap minus e less than peak less than p cap. Plus, if we know that our true proportion with lie between these two values. So what does this come out to be? It is 0.1350 point 135 less than people less than 0.152 0.152 Okay, now, how do it interpret this? We are 90% confident that this interval off 0.135 to 0.15 to actually does contain the true value of the population. Proportion off returned surveys. So this is going to be my answer.

All right, So we're given this set of eight points that comes from our sorry eight data points that come from a norm population. And we have some questions. Ask. So first off, what's your point estimate for the population mean or a point estimate for the population mean sorry. Equal sign is not technically after it. It's gonna be whatever sample mean is, uh, when you have these up, this becomes 10. 18 30 45. 50. There should be an 11 in here. My bad. So 10 18 30 45. 50 uh, 56 67 80. Yep. That was just a sandy check for me. Just making sure I had all the plot point that anyway, So All right. What's your point? Estimates. Come on. There we go. For standard deviation. Well, that's just gonna be the standard deviation of the sample, which, if you do the mathematics for which I'm not going to do by hand right in front of you, you're gonna get three points. 464 All right, now to find hour interval at and 95% confidence. So we want to find out margin of error in party and because we do not have a given population standard deviation. We only have ah, point estimate. Oops. We're going to use a tea interval. So it's gonna be tea time. Standard deviation over skirt and equals eight. We look a t star, we have n equals AIDS. So our degrees of freedom, which is an minus one, is gonna be seven. We check our tea table at seven degrees of freedom for 95% confidence. We get, uh, 2.365 All right, so this equals 2.365 times 3.464 divided by the square root of eight. Punch that in on our calculator and we get So this is about 2.8964 All right, finally, we're gonna constructor confidence Interval. All right, so Oops. There we go. So 10. Plus, he's simple. It's just 12.8 964 and subtracting out. You'll get some 0.1036 There's your interval. My pen's acting weird. Come on. There we go. And there you have it


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