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