Wetzel                                                                                                             

Math 120

Test #4

Read each problem carefully and check your work.  Work must be shown and legible for partial credit! 

1.)  An economist wants to estimate the mean income for the first year of work for a college student who has the profound wisdom to take a statistics course.  How many such incomes must be found if he wants to be 88% confident that the sample mean is within $500 of the true population mean?  Assume that a previous study has revealed that for such incomes, σ = $6000.   (10 points)

2.)  The tobacco industry closely monitors all surveys that involve smoking.  One survey showed that among 785 randomly selected subjects who completed four years of college, 18.3% smoke.  Construct the 90% confidence interval for the true percentage of smokers among all people who complete four years of college.  (20 points)

3.)  A sample consists of 24 TV sets purchased several years ago.  The replacement times of those TV sets have a mean of 8.2 years and a standard deviation of 1.1 years.  Construct a 99% confidence interval for the mean replacement time of all TV sets from that era.   (20 points)

4.)  A random sample of 100 babies is obtained and the mean head circumference is found to be 40.6 cm.  Assuming that the population standard deviation is known to be 1.6 cm, use a 0.05 significance level to test the claim that the mean head circumference of all two-month-old  babies is 40.0 cm.   (25 points)

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5.)  In a study of store checkout-scanners, 1234 items were checked and 20 of them were found to be overcharges.  Use a 0.08 significance level to test the claim that with scanners, less than 2% of sales are overcharges.  (round all work to three decimal places)

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