Quiz2_2009_Answers

Quiz2_2009_Answers - Question 1: A consumer research firm...

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Question 1: A consumer research firm conducts a poll of 21,994 people and asks them if they would purchase a new product. In the sample, 43% of the survey respondents answered “yes,” indicating that they would be interested in the new product. Given that 43% is the best estimate of the population proportion, why would we need a confidence interval? That is, what additional information does the confidence interval provide? Explain
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Question 1: Although 0.43 is our point estimate for the true population proportion, we know that this is subject to sampling error. A confidence interval gives us extra information beyond our point estimate (that is, our best guess), by giving a range of values to which we can attach a particular level of confidence. The width of this range tells us something about how confident we are in our point estimate. The wider the range, the less confident we are in our point estimate. The narrower the range, the more confidence we have that our point estimate is close to the true population parameter.
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Question 2 a Medical researchers interested in the effects of sleep on academic performance conduct a study in which they survey 44 undergraduate students. For each student, the researchers record the number of hours of sleep the student got on one particular night. The sample mean of this variable is 6.34. a. (2 points) Construct a 90% confidence interval estimate of the population mean, μ , of the number of hours of sleep a college student gets each night. Suppose that the actual population standard deviation for this variable is 9.88. Based on the confidence interval, does it appear that college students get less than the recommended 8 hours of sleep a night?
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/2 Where z Since the population variance is known, the confidence interval is the following: is the critical value for the standard normal distribution with the property that P(Z>z ) xz nn    1.645. Plugging in numbers, we get: 9.88 9.88 6.34 1.645 6.34 1.645 44 44 3.88 8.7 / 2 0.10 / 2 0.05. We can look this up 9 as z  
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Since 8 belongs to the confidence interval we are not sufficiently confident that students are in fact sleeping less than 8 hours. The estimate seems to suggest that students sleep less than 8 hours, but it can well be the case that it is just the result of sampling error. A bigger sample size, by
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Quiz2_2009_Answers - Question 1: A consumer research firm...

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