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3 points) The nicotine content in cigarettes of certain brand is normally distributed with mean (in milligrams) / and standard deviation 0 = 0.1- The brand advertis...

Question

3 points) The nicotine content in cigarettes of certain brand is normally distributed with mean (in milligrams) / and standard deviation 0 = 0.1- The brand advertises that the mean nicotine content of their cigarettes is 1.5 mg: Now; suppose reporter wants to test whether the mean nicotine content is actually higher than advertised: He takes measurements from SRS of 15 cigarettes of this brand: The sample yields an average of 555 mg of nicotine. Conduct test using significance level of a 0.01. (

3 points) The nicotine content in cigarettes of certain brand is normally distributed with mean (in milligrams) / and standard deviation 0 = 0.1- The brand advertises that the mean nicotine content of their cigarettes is 1.5 mg: Now; suppose reporter wants to test whether the mean nicotine content is actually higher than advertised: He takes measurements from SRS of 15 cigarettes of this brand: The sample yields an average of 555 mg of nicotine. Conduct test using significance level of a 0.01. (rounded to 2 decimals) (a) The test statistic (b) The critical value_ The final conclusion is There is not sufficient evidence to show that the ad is misleading: The nicotine content is probably higher than advertised



Answers

In the paper "The Smoking Cessation Efficacy of Varying Doses of Nicotine Patch Delivery Systems 4 to 5 Years Post-Quit Day" (Preventative Medicine, 28 pp. $113-118$ ), D. Daughton et al. discussed the long-term effectiveness of transdermal nicotine patches on participants who had previously smoked at least 20 cigarettes per day. A sample of 15 participants in the Transdermal Nicotine Study Group (TNSG) reported that they now smoke the following number of cigarettes per day. $$\begin{array}{ccccc} \hline 10 & 9 & 10 & 8 & 7 \\ 6 & 10 & 9 & 10 & 8 \\ 9 & 10 & 8 & 8 & 10 \\ \hline \end{array}$$ a. Determine the quartiles for these data. b. Remark on the usefulness of quartiles with respect to this data set.

We are doing men with new just many news just is a non parametric alternative to the T test for the difference between two independent means. This test is often used in situations in which the two samples had run from the same population off subjects but different treatments I used on each set. Men with new test is equivalent. Sorry, we call Will Coxon rank sum test voices as 34. We are required to test the hypothesis. H notes. The average nicotine content is the same. The alternates you the average Nicholson content. Jeffers. Yeah, we are given the rank some for brain A and rank some for brandy ranks some for friends. A six 88 on the ranks. Some for B is five 87 and A is called Toe End. Be is equal to 25 and Alfa is the quality of 0.1 We use this information to calculate the U Test new states where you a is a quote to, and a that's spread by envy. Last and be That's bad by N b. Last one All developed Sorry they wanted they to minus R. P. She is a part two 25 times 25 last 25 times 25 plus one divided by two my nose five 87 Is your quality 36 Okay. U p is a culture 25 times 25 plus change of life No times 25 What else? One. There are two minus 688 This is the culture. 262 You star is equal to the minimum between you A and U P which is a quality to you. Be 262 but then need to calculate that stuff. Is it stuff we need toe Catholics first The mean which is a quality in a multiplied by nb You got it. Bye. So she is equal to 25 times 25 qualified to is equal to 312 point life they understand activation signifies the call to the squirrels off in a multiplied by nb multiplied by n a plus and be glass one all divided by 12 silly which is a quality Soon the squirrels off 25 squared must abide by 51. You are by 12 Is it closed? 51 wind 54 And that stuff is a call to use the miners. The main divided by the Standard Division is equal to two 62 My nose 312.5, developed by 51 point life. Oh, is a cultural negative. Zero point 98 within need to find a privilege. He Well, that's stuff less than I called to negative. Zero point 98 is a culture using 23 for that's winning and the left hand sale we could two times zero point 16 35 which is a quote, sir, zero point 3 to 7 for two t within. Compare the Pavilion, which is zero point 3 to 7 with Alfa, which is opened 01 Since he she's a colt, zero point 3 to 7 is greater in Alfa, which is 0.1 We do not reject H nodes and conclude it's 1% liver up Significant. That's the average Nicholson content is the same ends. 1% live in off significant. The average nicotine content is the same

This question is looking back, it the data from exercise 37 relating to cigarettes. Um, it's also missed the first part. Work out the correlation. So here I've run out the r squared value which was given to the next. So search seven. As this is all we need to work out the correlation because oh, is that correlation? So we have all squared. So if we square it, although you else bad we're going to get the coronation. But here we've got a 10% on. We did it in a decimal. So the first thing to do is divided by 100 to get square root. No 0.92 fool. Which gives us an answer of no 0.9612 That is our corporation. That's all we needed to do for the first part. Beers asking us what it predicts about the average nicotine content of cigarettes that to stun deviations below average in tar. Now we need this correlation on as were two standard deviations below. We are two times nor 20.9612 Done deviations below the mean remembers not mean talk anymore. It's mean nicotine. And this give us notes at 1.92 to 4 standard deviations supporting him to know that we have a positive relations ahead. And when we did our square root you, this could have been plus or minus, as could any spare room. But if you look back at your ex so search seven, you'll see that the graph just, uh, rough little sketch of it grow off had a very clear positive relationship. So, with a positive relationship between two variables, you want a positive correlation, which is why there's no negative side hit on. It's also why are things will be moving in the same direction so far, Tar content is true. Center deviations below the meeting. Our nicotine content also needs to be to some dude rock 1.9 to to force and deviations. But the important below the me on for the last one pot. See if a cigarette is one standard deviation above main in in nicotine. What would we expect about the tar content? And again they move in the same direction? Onda. We need our correlation, So this time it's just one times that correlation. So no 0.9612 because they move in the same direction. Always, we canosa, both the main in, and it really is

This question is the last question that's looking at the cigarette data from excess 37. So you need the information in that question. So this one I've written out the important information from excites a seven on the top left that we're gonna need. So let's just get started with part A. They asked us to write the equation off the regression line now with any aggression. Nine. You're looking at an equation that looks something like this, which says our prediction of why is a plus b X So here we get told that are dependent is nicotine. So we know that our why huh is nicotine. And it's important that the hat on nicotine as well, because you need to show that you know you're aware that it's a prediction and not an actual value are a is our intercept on again that's given in the question, and then the last bit is B X. Now we know that X is going to be tar on in excess of seven. You're told that the coefficient of tar is not point, not 655 to, So you put the three piece information you were given in the same equation on that's it apart. A part B is asking us to estimate the nicotine content of cigarettes with four milligrams of tar. Now, this is just some substitution were short. Nick did. And so we do our equation. And where is his talk? We're gonna sub in that full milligrams so and we have the no point no 65 nor five to is going to give us no 0.262 boots on. If that is added to the no 0.14403 we get predicted nicotine content of not put 414 to 38 milligrams. That's what be moving on to Part C is offering us to interpret the meaning of the slope of the regression er in his context. So slope is ah curre efficient of tall which is no point. Not 65 nor five to now The slope is telling us about the relationship between tar Nichting. So for every one murga increase in tall, we would predict and no point no 6505 to the, uh increase in nicotine. So it just shows when teller in Crete an increase in talking 10 how much would we expect? The nicotine content on that would produce quite a small, quite shallow pseudo prohibit of being something that's a bit like that. If nicotine's on the why until was on exhibition a quite shallow slope and that is what it is in the context. So looking at D, it's asking us what's up one cent mese Now why instep going much a regression equation? Is this that hip? It's on no 0.15403 to on This is saying what we predict the nicotine content to bay if tall. Zero. Because it will be where, if we look back at my little sketcher, it'll be where the black this is crossed. So if even if there was no taller in a cigarette, you would predict the nicotine content to your point. One of 54 milligrams on that is what it's saying in the context, and that's what the answer big for that part on the final part is Part E. And it's saying if a new brand of cigarette contains seven milligrams a talk on a nifty never with the residual of minus 0.5 milligrams, what is the next in contact of this. We need our equation for residual. So residual is our actual value Month are predicted body, and we need a residual to equal minus 9.5. So if that is actual monitor scripted, if we do it every rain, they are actual value, which is what we want to this question. Is that predicted by a minus? No point. But what I've done there is moved the p to this side of the equation. So if we use that equation, we no need toe workout. What I'll put about he was gonna be. And that is exactly what we did before with a bit of substitution. So we have n well. Hey, uh, the smoke point No. Six. But fuck to this time of subbing in seven now and exactly the same Maybe did before. This will total North 0.6093 No. Four. Now we need to take this that substrates in hit. So we're gonna have our actual equals. No, 0.6 No. Three, My four minus no point. Fuck! This is going to give us an actual nicotine level, not 0.1094 runners rounded to four decimal places and that is everything that


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