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Comes Irom study of the factors that impact birth welght Here the varlable This data woman vislted physician during the fIrst trlmester of Visit Doctor Indicates wh...

Question

Comes Irom study of the factors that impact birth welght Here the varlable This data woman vislted physician during the fIrst trlmester of Visit Doctor Indicates whethcr whethcr a baby was bom weighing pregnancy: The varlable Low Weight Indicates under 2500 grams_ WelghtRow Total:! 39 1 Column Totals 30 S 9 39 Question to be Investigated: Does visiting doctor during the eardy stages of pregnancy secm be associated with lower incidence of low weight births? Complete the table to find the marginal

comes Irom study of the factors that impact birth welght Here the varlable This data woman vislted physician during the fIrst trlmester of Visit Doctor Indicates whethcr whethcr a baby was bom weighing pregnancy: The varlable Low Weight Indicates under 2500 grams_ Welght Row Total: ! 39 1 Column Totals 30 S 9 39 Question to be Investigated: Does visiting doctor during the eardy stages of pregnancy secm be associated with lower incidence of low weight births? Complete the table to find the marginal distributions, and then fII In the bottom right-hand corner. Identily the explanatory and response variabies. Let"$ set up the fractions we wlll use to make the comparison and draw our concluslons. To answer research question SUch . as the one we are investigating; we always compare the categories of the explanatory variable, s0 the totals for these categories will be the bottoms of our fractions: The tops of our fractions come from the one category of the response varlable asked about In the research question. Set Up the fractions and compute the percentages vou wlll use to make the comparison and draw your conclusions- What Is the percent decrease In low-welght births for women who visit the doctor regularly In the early stages of pregnancy? Draw conclusions to answer the question; Does visitlng doctor during the early stages of pregnancy seem t0 be ossoclated with lower incidence of low weight births?



Answers

One of the best indicators of a baby's health is his or her weight at birth. In the United States, mothers who live in poverty generally have babies with lower birth weights than those who do not live in poverty. Although the average birth weight for babies born in the United States is approximately 3300 grams, the birth weight for babies of women living in poverty is 2800 grams with a standard deviation of 500 grams. Recently, a local hospital introduced an innovative new prenatal care program to reduce the number of low-birth-weight babies born in the hospital. At the end of the first year, the birth weights of 25 randomly selected babies were collected; all of the babies were born to women who lived in poverty and participated in the program. Their mean birth weight was 3075 grams. The question posed to you, the researcher, is, "Has there been a significant improvement in the birth weights of babies born to poor women?" Use $\alpha=0.02$
a. Define the parameter.
b. State the null and alternative hypotheses.
c. Specify the hypothesis test criteria.
d.
Present the sample evidence.
e. Find the probability distribution information.
f. Determine the results.

Okay with this question um We are looking at a study that looked into um the effects of smoking versus birth weight of infants. And what they did in the study is they gave mom's a questionnaire asked them about whether or not they smoked, whether or not there the father smoked and then compared it to birth weight. And what they did is all of the moms. They separated the questionnaires for the smoking moms and non smoking moms and they focused on the questionnaires from the non smoking mothers. And with the questionnaires for the non smoking mothers, they then separated them into whether they said the fathers smoked or didn't smoke. So when we're looking at the data, um well let's just start answering the questions. A ask us was this an observation all study or an experiment? And this was an observational study. Yeah, and that's because there were no treatments imposed. Mhm. They didn't tell the father's um whether to smoke or not. Uh huh. Yeah. Yeah. They just were taking note of whether they did, so observational study. Um The explanatory variable is the variable we might think and explains what happens with the response variable, and they asked us to identify each of those. So the explanatory variable here was whether or not the father smoked and the response variable was the birth weight of the infants. And they ask us for part C. Um if we can think of any lurking variables now, a lurking variable is something that can be associated with the explanatory variable and the response variable. So the one thing that comes to mind after I thought about it for a second was the overall health um slash lifestyle of the family. Yeah. Yeah. And that would be because if the father smoked then the family overall might not have as healthy as a lifestyle, like maybe they're not as likely as a family unit to be exercising or to be eating healthy and that could also impact the birth weight of the infants. And there are other factors to race income. Um The health factor is what came to my mind first, and then in part D it tells us that they adjusted the results and they ask us what that means. And they just used statistics to adjust the final results yeah. Um to account far and hopefully eliminate um bias. So there were some things they were aware of and they made some adjustments to make the results basically more accurate. All right, part E ask us for summary statistics for both groups and what they ask us far. So let's go ahead and start a little chart for the non smoking group. And the smoking group were asked to come up with the mean with the median, Yeah. With the standard deviation Q one and Q three. And you know, they give us the data. What I did is I used my t. I. 84 calculator and you know there's instructions in the book how to use different types of technology, but this is what I had handy. So I put in the stat list, so stat edit I put the data for the non smoking fathers, the kids, birth weight enlist one, and then for the kids with the smoking fathers, their birth weights in list too. And then in order to get summary statistics, once you have all that data and I can just show you, I put it all in, it keeps going um you can calculate your summary statistics. So I go back to stat and this time I'm going to go to the drop down menu for calculate and I'm going to calculate one variable stats, which is number one, and I'm gonna start with the first list, this would be the summary statistics for the kids with the non smoking fathers, and we just go down to calculate and hit enter and I can see the mean is the X. Bar is his first value, the 36 65.5 s f X. Is my standard deviation. Then I have minimum Q one median Q three max and then I can do the same thing. Um I'm just going back to calculate back to one variable stats but this time I just need to change the list, I want to do the same thing for the smokers and that gives me those same statistics for the smokers. So let's write those down. Mhm. So for the non smokers then um Mean was 3:36 65.5 and this is grounds and then the median was 36 93.5. Standard deviation was 3559. Q one was 34, Q three was 39 76. And then for the smokers 34 64, 34 75 4 52.6 31 29 38 07 So there are my summary statistics for part F. It asked me to Interpret Q. one. These values For both the non smokers and the smokers. So let's think about that Q1 is our first quartile. And you know if you have a it's just Draw this this would be Q. one here. So below Q. One this is 25% of the data. So if I'm interpreting Q. One that would mean for um the non smoking fathers, 25% of the infants had a birth weight below That first quartile 34 36 g. And then for the smoking fathers, 25% of the infants had a birth weight. Okay Below 3129 g. So already we're beginning to see for Q. One. The birth weight was lower right for the smoking fathers than it was for the non smoking fathers. And then for G. It asked us to create um side by side box plots. And again I used my technology for this. I had already put the data into my list. And so I used the stat plot. I've turned on both of these plots Plot. one is list one and I've changed it to a box plot. And let me just enter plot one. So you can see so you make sure that you are toggled on. You make sure that you have highlighted and selected the box plot. And then you choose the list that you're plotting. And then I did the same thing for a plot to accept the list that I'm plotting for. List two is the second list. The um smoking fathers. When you're using A. T. I. 84 to graph. If you'll remember to hit zoom nine Zoom is all the preset windows, it'll make the viewing window real nice. So I can see the blue is the non smoking group and the red is the smoking group. So we just need to um create that copy that onto our paper. So let's go ahead and do that. So I have, We need a scale. We're going to go 3,030 504,000 Uh 40 500. Mm. Uh You know the one thing I didn't show you, Let me come back up here, but I did to put this onto my paper is I want to I need to kind of know where the tick marks are so I can fit it onto the scale. If you hit trace, notice the cursor here is blinking on the blue graph and as I arrow left and right, it's going to show me the five number summary. Now. Could have also written that down when I calculated my summary stats, but I forgot to so I can do it here. So the minimum Is 29 76. Q 1 34 36 median q three max to get the same thing for the second box plot. Just narrow down. The cursor will jump doing up and down. It jumps between the two graphs and arrowing left and right. Shows you your five Number summary. So however you get it, you need those five number summary so we can make our box plot. So for the smoking group, um Let me find my numbers for the smoking group. The minimum was about 27 46. Um Q one was 31. Q median was about a little bit less than 35. Q three was 38 And Max was 42. So I connect the lines here to make my box Go to the maximum for Mike Whiskers. And then for the smoking group, 29 76 was the minimum. 34, was Q one. 36-93 was the median, 39 76 was third quartile in 43 was max. So when we look at the comparative box plot, we can see and let's label it. This is the non smoking fathers, this is the smoking fathers. So there does appear to be evidence that the birth weight for the infants with smoking fathers is less than for the non smoking. Because if we're if we're looking all of the values for the smokers, right, the minimum for the smoker is less. Q one is less, median is less. Q three is less. Max is less. So it does appear that birth weights for infants with smoking fathers is less than that of infants. Yeah. His father's don't smoke. Okay. Yeah. Mhm. Okay, there you go.

Right one. This is the estimated equation where lock of birth weight is regressed on N P V I. S and N P V I S square and PVS represent prenatal visits. We have 1700 observations are square is .021 and are square Adjusted is .0-0. The estimated coefficient on prenatal visits square is minus point Triple zero for 3. And this one is highly significant. As you can tell from their value of the standard error. If we calculate the T statistic, which is the estimated coefficient divided by the standard error, we will get almost minus four. This is a very high T statistic. Yeah, Prenatal in level. This one is also significant and the positive and negative coefficients indicate a hump shape relationship between locker birth weight or birth weight and prenatal visit. We can find the turning point which is the value of prenatal visits. That optimize birth weight maximize worth way in exact. We even set their first derivative of locka birth weight with respect. You prenatal visit 20 and you can find the turning point. M. P. V. I. S. Star as the result of taking .0189. That is their coefficient on NPV is divided by two times the estimate on and T V. I. S square .00043. And you will get 21 point nice seven. So roughly 22 is it in the sample? About 89 women had at least 22 prenatal visits. Part three asked you to explain the hump shape relationship between pre natural visit and lock the birth weight. So while prenatal visits are a good thing to do to prevent low birth weight. Which explains their positive coefficient on prenatal visit at large value of prenatal visits meanwhile, indicates a pregnancy with difficulty possibly. And that explained there negative sign on NPV I. S. Quadratic term. Yeah. Yeah it should be part three, not for The next part is Part four. And you win add to The equation in part one, mother ache and mother X square. You still have roughly similar result for prenatal visit, same signs seem significance. See and from other age you observe a similar hump straight relationship. These coefficients are highly significant. Our square is now .0256 and adjusted our square is .0234. You can find the value of mother age that maximize birth weight. Again you can set their first derivative of locker birth weight with respect, you mother age 20 and you can find mother age square to be Roughly roughly 31. There are 746 women in the sample Who are at least 31 years oh R five Because they are square of this regression is .026. So these variables, mother age and prenatal visit explains roughly two points 6% of the variation in locker breath, wait, it's not very much part six. We keep there right hand side variables, but on the left hand side we replaced Laka birth weight with birth weight in levels. Running with this regression, we obtain an R square of zero point Z. Room one 92 So this this are square is not comparable with with the R square from The model in part four where we have the lock of birth weight as the dependent variable. So to make the model with lock of birth weight as the dependent variable comparable, we need to find another value of our square. We will compute the correlation between birth weight in levels and the exponential of the fitted values of the locker birth weight. Like a birth weight fitted values come from module in part four. The correlation here is 11362. And that gives and our square between birth weight and the exponential of the log birth weight fitted to model for to be coin one 0.1 86 You should know that this value is the exponential of a uh linear combination. The linear combination of prenatal visits and mother H. These are square is smaller to our square. We get when we regress birth weight in levels on the explanatory variable. So the model with birth weight level is better. It fits the data slightly better. Then the model with the law of birth weight as their dependent variable.

Once again welcome to a new problem. This time we're dealing with regression elements, and there's always a powerful aspect to looking for relationships. Uh, relationships between between quantitative variables. And in this sense, you're saying you have your ex, which is your independent on. Then you have your while, which is your dependent from contextual aspect. Your X variable is the explanatory variable and your wife variable is your response variable. So you want to see the impact that the explanatory variable cousin the response variable. And towards that, you tend to build a model where we do have slope coefficient. So this is a simple linear regression model where the e is our era and the being art is our intercept. So the point to each the value of X zero so we don't have any influences, we're gonna make it zero on, then, of course, beta one is your slope coefficient. This is a slope coefficient that relates that relates your ex and your wife value. So in this particular problem were given, um, a regression equation. It's a simple linear regression equation, um, are based off of white hot equals to bait or not, plus beta one x y hot is the predicted, uh, why value? Because if you have a model with a bunch of data points, there's gonna be a straight line which estimates theme, the data points. And since the straight line is not, um, is based off of a sample, it's gonna be a predicted equation. So in this particular problem, we have an equation that relates the birth weights off Children. They have a heart to talk of it because it's predicted and then three intercept is 11 19.77 minus zero point 514 mm x. But in this case, X is cigarettes. So So it's a relationship between bath, wheat and cigarettes. Um, so this one stands for, um, the theme the infant in front birth weight. Now, this is the infant bath. Wait, that's your wife? That's your widebody wife values the infant about three, but the who responds variable off the dependent variable and then the independent variable C I. G. S. That stands for the the average number off cigarettes. So this is the average number of cigarettes, uh, smoked for a day during pregnancy. So, you know, we want to see if there's a relationship between these two were given a regression model theme. The first question is, uh, determined the birth weight when the mother smokes zero cigarettes during pregnancy. And then the second thing is, how about 20 cigarettes during pregnancy? We also want to check Compare the outcomes off these to or inputs. And part B, I was saying, is the relationship. All of the same is the relationship between our cigarettes and both weeks causal. So, by co so we mean that does smoking during pregnancy. Perfect biathlete. There's smoking during pregnancy effect about a week and then put seed Hmm given above wheat Hoff 1 25 ounces. How many? How many cigarettes would? No. How many cigarettes would cause this out? Yeah, okay. And January 14 through the proportion mhm non smokers in this sample. The proportion of nonsmokers on this sample is 185 Um, how those is help being from outcome proxy. So these are the questions presented, and we're just going to jump in and figure out what the solutions are. So if we have, uh, the number of cigarettes, if it's zero, then the equation becomes, but wait, it calls to 1 19.7, minus 0.514 and then you plug in zero. And obviously you could see your outcome is 1 19.7 ounces. And this happens because, uh, this part is going to cancel out. And then in the second part, was saying if the number of cigarettes is 20 will repeat the process with about weight. But now you're plugging in 20 paseo result right next to the slope coefficient. And so you're gonna end up with, um, one or nine point 49 you're gonna end up with mhm 1949 So we just want to check that to make sure that we're getting the right answer. Yes, one of 9.49 So then that's the number of answers you will have. That's what a mm. And you can see that the the relationship between smoking and birth weight his inverse as mothers smoke okay more during pregnancy there, Childrens or influence? Let's call it influence on Children. Their influence birth weight declines on on. Then, in the second part of the problem way, uh, looking to see if there is a causal relationship when will say models typically smoke before the onset off pregnancy. Therefore, okay. Their food. Mm. The relationship between okay, both wheat and, uh, smoking is causal. So there's a causal relationship between the two other factors. Other factors can a fake both wheat outcomes, including uh huh. Mothers help during pregnancy. Yeah, Mother's health during pregnancy. The uh huh. Environmental fact is searches evolution when mothers in cu no and so on and so forth. Who say multiple regression models can include these extra variables can include these extra variables. Hmm. But smoking still, please? Uh, significant coz. Oh, role on influence, BlackBerry and then input. See, But see was saying, uh, given the birth weight given the bath fleet is 1 25 ounces. We want to predict how many cigarettes you're going to get off of that. So we do know that the equation looks like this 1. 19.77 When? 0.546 Want to predict this? So plug in 1 25 ounces on and simplify the equation. For since e was subtract mm 1 19.77 on both sides. And then we end up with way end up with negative 0.514 since equals two. So if we subtract those two numbers, we get 1 25. When this 119 from 77 you get 5 to 3. Wife went to three ounces. Hmm. And then we divide both sides by 0.54 For some reason, we're ending up with a negative number for six on There is a meaning for that. So you say on and okay, having, uh, negative number for cigarettes is impossible. Uh, the reason Mhm being. But, um, the values provided search us 1 19.77 ounces. Represent, Yeah. Outrage numbers. Wine. Uh huh. Uh, zero cigarettes. So average numbers when you have zero cigarettes, and this is this is the best of rich. Mm. This is the best average. And then finally, the last step off the question, Hmm. Uh, non smoking pregnant on smoking. Pregnant mothers represent 0.85 of all pregnant. Okay, brothers in the summer. That's, like, 85%. So looking at what just happened in, But see, how can we reconcile this with that housing? Housing more? Mm hmm. Smokers in the sample food make most sense. Uh, in the study. It's gonna make more sense in the study. Uh huh. Since it provides the march needed variation in the explanatory viable, much needed variation in the expand to invite seats. Mm. Helping us helping us, Gertz? Uh, most practical. Practical average. So the mm intercept. Uh, where would say where? The intercept Where the intercept represents mhm. Both wheat off in funds from land smoking mothers. Mm. Increasing non smokers. You? Yeah, will will say non smokers of non smoking. Increasing non smokers will alter positions, right. Both the average birth weight. Okay. Off infants to be good, find you than is currently presented. So once again, we had a problem. And in this particular problem, we had to identify for issues connected to bath weights. Fast one waas Uh, what's the what's the ounces when the weight is 01 19.77 and then what's the way? The ounces when the weight is 21 or 9.49 And then, um is the causal relationship? Absolutely. Because we get to see that our mothers will usually smoke before they get pregnant. So then once they get pregnant, we see that the habits of smoking effects the bath weights by having a lower bath with theme the general population of non smokers. Even if you have a multiple regression model, I mean, including all the variables you'll still see. The smoking has a stronger aspect. And but see, we've ended up finding a negative number of cigarettes, which is not possible since you can never have a negative number of cigarettes. And the reason why we're having that is because off the proportional, um, non smokers the mm proportion of non small because that from being 0.85 on the question is, is this helpful in the problem? Does this help from the problem? MM. In the sample. Obviously wanna have more smokers, and that provides more variation on give us most accurate results for non smokers on and on, the intercept takes a larger value, so I hope you enjoy the problem. Feel free to send any questions or comments and have a wonderful day


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