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A study was conducted to study college students who smoke tofind if there was a relationship was between number of cigarettessmoked per day and parental smoking sta...

Question

A study was conducted to study college students who smoke tofind if there was a relationship was between number of cigarettessmoked per day and parental smoking status. The studyrecruited 300 college students who currently reportedsmoking. In the study, the adult children of smokers smokedapproximately 4 cigarettes more per day than the adult children ofnon-smokers. The 95% confidence interval for the differencewas 3.4 to 5.3 cigarettes per day. If we wanted to reduce thesize of our confiden

A study was conducted to study college students who smoke to find if there was a relationship was between number of cigarettes smoked per day and parental smoking status. The study recruited 300 college students who currently reported smoking. In the study, the adult children of smokers smoked approximately 4 cigarettes more per day than the adult children of non-smokers. The 95% confidence interval for the difference was 3.4 to 5.3 cigarettes per day. If we wanted to reduce the size of our confidence interval (that is, reduce the width), which of the following would help? Select all that apply. A. None of these will have an impact on the size of the confidence interval. B. Recruit more college students to participate in our study. C. Perform a new study with less college students. Redo the study with the same number of adults, but include more than just college students. None of these will have an impact on the size of the confidence interval. D. We could calculate the 99% confidence interval instead. E. We could calculate the 90% confidence interval instead. F. Redo the study with the same number of adults, but include more than just college students.



Answers

According to the National Center for Health Statistics, the average height of females in the United States is 63.7 inches with a standard deviation of 2.75 inches. Using the heights for the random sample of 50 female American health professionals in Exercise $8.1,$ page 344:
a. Test the claim that the mean height of females in the health profession is different from 63.7 inches, the mean height of all females in the United States. Use a 0.05 level of significance.
b. How is "there is a significant difference" (rejection of the null hypothesis) revealed in the confidence interval formed in Exercise $8.127(\mathrm{a}) ?$
c. Explain how the confidence interval formed in Exercise $8.127(\mathrm{a})$ could have been used to test the claim (hypothesis test) of part a that the mean height of females in the health profession is different.
d. How would "there is no significant difference" (failure to reject the null hypothesis) be revealed with a confidence interval?

Okay, now in sustained care. The first case. Let's take off the sustained care Sustained care. Okay, What is going to be my pick up? My peak at is 0.8280 point 828 Okay, Now my end is 1 19 in is 1 98 and I want a 95% confidence level. Which means my Alfa by two is what my Alfa by two is 0.0 to fight. So Z alphabet to will become 1.96 All right. We already know the formula for e the formula for he is going to be Z Alfa by two multiplied by rude over peak cap into one minus p cap or we also I just ask you cap upon in right. Do we have all the values? Yes. So what is goingto be the value of E? If I substitute these, I get my value of 0.5 to 6. My E in this case turns out to be 0105 to 6. Fine. And how do I write the confidence interval it is given by this. Okay, now these are the two formulas which are required here. Okay, So what is my confidence in double for the first case, 77.54 to 88.6 This becomes 77.54% to 88.6%. Okay, this becomes for the sustained care. Now, what about the standard care for standard here for standard game over here. My P cap is 0.6 to 8. 0.6 to 8. This is my peak app. My in is equal to 1 99. My n is equal to 1 99. And my Z Alfa by two is 1.96 Same as before. Z Alfa by two is equal to 1.96 which is the same as before, right? This is 1.96 So again substituting the values to get the answer for E my He turns out to be 0.672 0.672 What am I using? The same formula. And now I will use this formula to find the interval. And what is the interval that I'm getting in this case? The interval that I get over here is 56.8 to 69.52 56.8% to 69.5 2%. Okay, so what can I say? The confidence interval for the sustained care lies completely above the confidence interval for the standard care, which indicates that the sustained care is more effective than the standard care. Sustained care is more effective, sustained care is more effective and this is going to be my answer.

This question were asked to identify the population and sample based on different scenarios and tell whether or not they can be used to create a confidence interval. So let's first start off by just defining the variables. So we have P, which is the population proportion and P hot, which is the symptom, the sample proportion. So in taste A our population will be all the cars, whereas the sample size is going to be the cars stopped at the certain checkpoints and like we said, p as the population proportion. So in this case, is all cars with safety problems, and P hot is a sample proportion. So these air the cars that are actually seen with safety problems. So we can further calculate P hat by using the numbers given. And we know that there are 14 of 134 cars stopped have at least one safety problem, so that number ends up being 0.1045 Weaken further transfer that into percentage form and we get that it's 10 points 45% as RP hot volume and were also asked whether these methods can be used to create the confidence interval. So when a sample of data is representative, then it can be used to create a confidence interval and in this case it is because it's sampling all cars. For case be, we are going to find the population and sample once again for the population. We have the general public and for the sample, it's people that are logged into the website. We can further define them as P being the favor. The people in favor of prayer in school where us The sample proportion are the people that voted in this poll who favor prayer in school, we can calculate p hot with the given values were at 488 over 602. We get 0.81 and making that into a percentage value, we get 81% toe. Decide whether or not the sample can be used. We can Onley consider people logging into the website for this case. So in a way it's a bit biased and non random. So you're unable to apply the methods to create the confidence interval in Casey. The population is the parents at school and the sample is the parents expressing opinions through the question here. So the population proportion are all parents who favor the uniforms, whereas the sample proportion P hat are the respondents favoring uniforms. We can calculate the P hot value based on the numbers given 228 over 380 and that gives us a value of 0.6 that can be converted into a percentage of 60%. And since there were 1245 surveys sent home but only 380 returned, there is a complication of non response bias. And so you would use these methods with caution if creating a confidence interval. And the last part D were given a population of students at college, and the sample size is the 16 31,632 College admits the population proportion are all the students who will graduate on time and P hot the sample proportion as the students graduating on time that year. So based on the given values, we have 1388 over 632. Actually, this number is supposed to be 16 32. Sorry, and so based on that we get a value of 0.85 and that could be converted to 85% based on this value, and the sample data for this case was pretty representative. So since it is representative, you can apply these methods to create a confidence interval.

Yeah, friend. Is there a difference between how competence, social acceptance and attractiveness influence our self esteem? That's what this question analyzes and we're going to be using confidence intervals to look at the differences between these. So I've written our confidence interval formula for quantitative data and I've plugged in our means are standard deviations and sample sizes for all the groups and for an 85% confidence level with degrees of freedom of 14. RtC is 1.5 to 3. Now as we go and calculate here, the difference in our averages between competence and social acceptance is is 0.52 And then our margin of error for this is 1.8665 And when we add and subtract 0.52 plus or minus 0.1 point 8665 we're going to get a confidence interval from negative 1.3465 up to positive 2.39 Okay, now notice in this interval zero is inside of this interval. So there is a good chance there is zero difference between competence and social acceptance for the second question where analyzing competence versus attractiveness. So when we run our calculations here, the difference in the means is 1.96 and our margin of error is 1.9 which leads to a confidence interval of 0.6 to 3.86 This interval is entirely positive so it definitely appears like there is a difference between competent, how competence and and attractiveness influence is our self esteem. And in our last one where we're comparing social acceptance and attractiveness, the difference in the means is 1.44 and the margin of error comes out to be two point oh 47 So our confidence interval here runs from negative 0.607 to positive 3.487 and zero is in this interval. So there is a good chance there is no difference between social acceptance and attractiveness. So the only two groups where there is a difference, is let her be comparing competence and attractiveness.

In problem 16 we given from national statistics. But 23% of men spoke while 18.5% of women's movement. And we also given that a random sample or 118 men and 150 women sticking and 50 out of 180 smokers, one men and that lying out of 150 women. What's more because so they're going to be constructing 98% confidence interval for the true difference in proportions off male and female smokers. Then we're going to make a comment on this interval to see whether it supports the claim that there's a difference in these two proportions. So so the fasting will do is to give their the Akbar This is there now I provinces and the alternative. But this is on this case. Anamika. This is here's p one equals p two. That is to say that the proportions are equal and they have time to be. But this is is P. One is not a call to p two and things were getting the 90 8% confidence interval. The level of significance would be 0.2 So our Alpha 0.2 And for two tailed test. The critical value is two point three two seeks. Next. We work out the proportions for men and women smokers. So for men, the proportion he is 50 out of 118 and that simplifies to 0.27 feet. The proportion of women smokers is that nine out of 150 which equals 0.26 Next, we substitute the values of P one Heart and Peter Hart into the equation to obtain the 98% confidence interval. So we have a P one hearts 0.278 minus B to heart, which is Europe to six, plus or minus. The critical bunion, which is 2.3 to 6 times the square it off P one hunts your 0.278 times. Q one heart with his one meters, their 0.27 neat divided by N one cities 118 mass. P. Two hot 0 to 6 times key Too hot to choose. One rain is your 10.26 divided by entities, which is 150. So you can simplify on all this using a calculator and that you will get the difference here to be your point zero one it and the right hand side of expression be zero 0.70 point 114 Now we can add 0.14 or subtracted from 0.18 so we will obtain zero point 018 minus 0.11 It's less than the population proportion difference. P. One minute speak to just less than 0.18 plus zero point 11 and when you simplify your team, the following the lower limit is negative. Zero point zero 96 on the upper limit is zero point 132 So this is the 98% confidence interval. So we need to make a comment about this interval on. One thing that you notice is that the intervals are contains zero. So when it contains zero, it means that there's a possibility that the proportion the difference in the proportions would be zero. And because zero is contained in this confidence interval, we come conclude that the confidence interval does not support the claim. That is a difference in their proportions off male and female smokers


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