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Cigarette Smoke Use the data in Table $2-16$ to make a stem-and-leaf display for milligrams of nicotine per cigarette smoked. In this case, truncate the measurements at the tenths position and use two lines per stem (see Problem 5 , part a).

The first thing you want to do when you're making a stem and leaf plot is to take the data set that you're given and order it from lowest to highest or from smallest to largest. That's what I've done here. The next thing we're going to do for this problem, as we're going to truncate each of the data, points to the tense place what that means. So we're going to take each data point like we'll start with the 1st 10.13 and this will become 0.1. We'll take 0.40 This will become 0.4 0.42 will become 0.40 point 57 will become 0.5. Notice that we're not rounding Mhm. We are truncating. We're truncating at the tents place. That means we're just chopping off the hundreds. Place 0.61 becomes 0.6. Now we have our data truncated at the tents place next to make our stem and leaf plot. We are going to have a column for stems in a column for our leaves. We are asked to use two lines per stem. So what does that mean? That means for each stem, we will have two lines. So our first stem is going to be zero because our first data point is 0.1. So our first stem is zero and we're going to have two lines for each stem. So I'm going to write another zero in the second line or our leaves leaves zero through four, go in the first line and leaves five through nine. Go in the second line for our leaves, leaves zero through four, go in the first line and leaves five through nine. Go in the second line. So let's start filling in our leaves. So our first leaf is going to be a one because our first data point is 0.1. So our stem was a zero. Our leaf is a one is basically the decimal is at the line. Our next leaf, We're going to go to our next data point, which is 0.4. So we're going to write for for our next leaf. For our next leave, we'll go to our next data point, which is 0.4 again. So we're going to write another four our next data point is 0.5. So we need to go to the second line because remember, that leaves five through nine go in the second line. So for data 90.0 point five, we'll go to this line the second line, So we will put a five year for that leaf. Next, data 0.0 point six will put a six year that data point. Next data 0.0 point six. So that's another six. Next data point is 0.6, so that's another six. Next data point is 0.7, so that's a seven. Next data point is 0.7. So that's a seven. Next data 0.0 point seven. So that's a seven next 0.8. So that's an eight. Next is 0.8. So that's an eight next to 0.9. So that's a nine. Our next data 0.0 point nine. So that's a nine. Our next data 0.0 point nine again. So that's another nine. Now we go on to our next data point, which is going to be 1.0, so we're going to have to add a new stem, which is going to be one. Remember, we're using two lines per stem, so let's go ahead and write another one. So for this data 0.1 point zero, our leaf will be zero. Next data points 1.0 are leaf is zero. Next data 0.1 point zero. That's another zero. Next data 0.1 point zero. That's zero. Next data 0.1 point zero's. That's another zero. Next data 0.1 point zero. That's another zero. Next data 0.1 point zero. That's another zero. Next data 0.1 point one. So that's one Next data 0.1 point two. So that's a two. Our next data point is 2.0. So we're going to have to add a new stem just going to be too. So notice that we don't have any stems for the second line of one because we don't have any stems that are five through nine, so this will be blank. You can either leave that blank or you can erase it. Our next stem is going to be a two for our final data point, so we'll write to and the data point is 2.0. So our leaf will be zero, and that is our stem and leaf plot

In question seven. Here we have to figure out what the P value is for the test of the hypotheses where the slope of the least squares regression line equals zero. When then the alternative hypothesis is that the slope is positive. And so one thing that you want to take note of initially is what the P value is from the computer output table that's been given. And so if you take a look at the column that's labeled with P, and you go to the row that lines up um with the explanatory variable X. And go across there. This P value is the first number you want to take note of, but that's not the answer for this question. That is the answer to the question. If the alternative hypothesis where that beta were not equal to zero, which is a two tailed test. So if that's the answer for a two tails test, and I want to know what the answer for a one tailed test is, I have to take the P value that is given and divide it by two. And so dividing that by two gives me 0006 and so that is the p value for this question, and that gives me answer choice Hey?

Okay, So for this problem, we've been given various sets of molecules and we've been given the last percent of all the constituent elements within these molecules. So for the first molecule, we've been given that it has a mass percent of 95.21% carbon and 4.79% hydrogen. And we're gonna assume make this easy, that we have 100 grams of this substance here. So that makes us that we have 95 grams that if I went to one grams carbon and 4.79 grams of hydrogen and this makes it easy because now we can find out how many moles of each thing you've constituent element. Carbon and hydrogen there are within this 100 gram sample of are unknown Well of ah are known element. But of unknown Mr Key metric ratios between the two elements here, So we're gonna do is we're gonna divide this each of these by the atomic mass of the elements. So 95.21 is going to divided by 12 1 clams for more. Um, this is gonna be divided by 1.1 grams per mole And that gives us, uh, one point. Oh, sorry. Not 17 0.93 moles of, uh, current. And it's going to give us for those 7.3 moles. There are 4.79 moles, most of them. Okay, And now that this is the total number of moles of even as we have, we can divide these. I'm gonna divided by the smaller of the two years. I mean, invite each one, but smaller that year. So when we divide each of the use by 4.79 we get that we have for 4.79 moles of hydrogen. We have a ratio of one. So for carbon here, hydrogen, that's gonna be one hydrogen for carbon. We're gonna have 1.66 which we can say it approximately equal to 5/3. And this makes it easier to think about right, because if you have 5/3 of a carbon for everyone hydrogen, well, we know how to turn that, you know, from a fraction to a manager, we just multiply by three. So we take this ratio here, and we're going to multiply in both numbers by three. And that gives us that we have five carbons and three hydrogen and these air nice images here. So that means that we have found our empirical formula, since they can no longer be reduced to a smaller energy while still maintaining the same relationship between the two. So but that we say that our formula for this compound is C five each three and that is our first. Now for our second problem, we check if, like in school. Well, the trouble scrolling here and see if you fit in. Right. So for a second problem, we've been told various mass percents of various elements within this compound for supposed to say I'm just gonna write this out, assuming we have 100 grams of this compound. So those percents basically just turn into cramps. So we have 30 30 eight, 37 grams carbon. We have 1.49 grams hydrogen 50 to 1 to h grams of chlorine, and we have 7.86 grams of oxygen. Okay, And now we're gonna divide all these by the molecular weights. So this is going to be divided by 12. This is going to be divided by one. Is going to divide it by 35 5 less You're gonna be divided by 16. Good. And it's not incredibly important that we use all the decimal precision that were given in our periodic table because, you know, there is a fair bit of rounding and like, Well, that looks close enough when doing these incorrectly. So when we do this, we get the following. So this is going to be about 3.2. This is gonna be five. This is going to be once I began and he's just going to be easier. So now we're gonna multiply these by two. Because if we do that, we see that we turn a lot of these into imagers. So we multiply them by two. And that gives us certainly not 366 for 33 and one. So now we can look at this and say, OK, well, we've three nice imagers here that we don't need to really like multiplied by any decimals, invest with right, so we can just say Okay, we have these imagers. Well, let's not worthwhile by a decimal. Then what's the most about another manager and then we look at the we can look here at the 6.4 and say, Well, that's pretty close to 6.5 and within, You know, our tolerance is here. Where were given all these Kind of, like hand waving and imprecision with decimals We can say that. Okay, let's just time off my to. So that means we have 12.8, which I'm gonna call 13 because it's really close to 13 and for are available precision here. That's gonna That's going to be enough for us. So we have six, six and two, and these are nice senators. You. So this is going to be our final ratio for our various elements. Right? So this is gonna be carbon 13 hydrogen six, but we have Korean six and oxygen to. And then this is our final chemical formula empirical formula for this company.

All right, you guys. So, first we need to start by identifying are null and alternative hypothesis. I know hypothesis that continent is that continent should be the same in both smokers and non smokers and alternate hypothesis is that continent should be greater in the smokers. So that is denoted by that, uh by this right there. And then the next thing we're going to do is this we are going to um find the f statistic and the P value. So I'm going to find the statistic and the P value. First, we need to jot down our standard deviations are first standard deviation is 1 19.5. Our 2nd standard deviation is 62.53. Okay. And then we need to find our s square there. S one squared is the bigger standard deviation times itself. Let's go ahead and do that. And so what this means here is I'm asking the google sheet that I input, I'm putting the data into the calculator. For me. You do that by first pressing the equal sign. An equal sign in google sheets, tells you, tells the google sheet to calculate something. You then take what you want to multiply and multiply by itself, by the way. An asterisk and google sheets means multiply And there's our first s one squared value. RS two squared value is calculated the same way. Except we use our smaller standard deviation. And then to find our f statistic, we nearly divide the two by pressing an equal sign, clicking on the larger one a slash for divide and divide it by the smaller one. And that is our f statistic. Okay, so they're they're statistic is right there. So now we need to find our p value. Okay, R p value can be calculated in this way. So first press the equal sign. Then you're going to tell the google sheet to do an F distribution. So f dist open parentheses and you need the input three values. The first value is the f statistic. The second is the degrees of freedom for S one squared. So S one squared has um s one squared is the group of smokers. So in this case um Since they had 40 people, you're gonna put 39 in because degrees of freedom is the number of people -1. And we're also going to input 39 for the non smokers because the non smokers also had a group of 40 people. So again, you're gonna input um degrees of freedom, which is N -1. We then hit enter and RP value is significantly smaller than 0.05. And so what we're going to do is we're going because it's so small, we're going to reject the null hypothesis. Alright, So that's part A. All right. And then let's go ahead and look at part B. Part B. Um They're going to go ahead and look at the CO 29 I think that's where you say code nine, measurements for the non smoking group and there are a lot of values that are zero, while the majority of values are zero. But then we have some very very large values as well. So this does not look normally distributed. Um This does not appear to be a normally distributed population. In fact, it looks skewed left. If I graph it would look skewed left not normally distributed. And this greatly affects the results in part A. Because an F distribution needs to have a normally distributed data. This greatly affects the data in part A. As an F statistic yeah, needs and put it in all caps. Um Normally distributed data.


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