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Accelerated Math 3
Sample Size for Confidence Intervals
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1. The Washington Vending Machine Company must adjust its machines to accept only
coins with specified weights. We will obtain a sample of quarters and weight them to
determine the mean. How many quarters must we randomly select and weigh if we
want to be 99% confident that the sample mean is within 0.025 g of the true population
mean for all quarters? Assume that the population standard deviation is 0.068 g. n =
50
2. A psychologist has developed a new test of spatial perception, and she want to estimate
the mean score achieved by adult male pilots. How many people must she test if she
wants the sample mean to be in error by no more than 2.0 points, with 95% confidence?
An earlier study suggest that   21.2 . n = 432
3. To plan for the proper handling of household garbage, the City of Providence must
estimate the mean weight of garbage discarded by households in one week. Find the
sample size necessary to estimate that mean if you want to be 98% confident that the
sample mean is within 2 lb of the true population mean. For the population standard
deviation, use the value of 12.46 lb, which is the standard deviation for the sample of
62 households included in the Garbage Project study conducted at the University of
Arizona. n = 210
4. In an insurance company study of New York State licensed drivers’ ages, 570 randomly
selected ages have a mean of 41.8 ears and a standard deviation of 16.7 years. Use the
sample standard deviation as an estimate of the population standard deviation and
determine the sample size necessary to estimate the mean age of New York State
licensed drivers, assuming that you want 99% confidence and a margin of error of 0.5
years. n = 7403
5. In a study of physical attractiveness and mental disorders, 231 subjects were rated for
attractiveness, and the resulting sample mean and standard deviation are 3.94 and 0.75,
respectively. Use the sample standard deviation as an estimate of the population
standard deviation and determine the sample size necessary to estimate the population
mean, assuming that you want 95% confidence and a margin of error of 0.05. n = 865
6. The standard IQ test is designed so that the mean is 100 and the standard deviation is 15
for the population of normal adults. We want to determine the sample size necessary to
estimate the mean IQ score of statistics instructors. We want to be 98% confident that
our sample mean is within 1.5 IQ points of the true mean. n = 542