7.2b Find sample size.notebook
April 19, 2018
A survey of 35 adults found that the mean age of a persons
primary vehicle is 5.6 years and the standard deviation of
the population is 0.8 years. Find 99% confidence interval of
the population mean.
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7.2b Find sample size.notebook
April 19, 2018
Chapter 7 Section 2b
Determining Sample Size
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7.2b Find sample size.notebook
April 19, 2018
Chapter 7 Section 2b
Determining Sample Size
If a college president asks the statistics teacher to estimate the
average age of the students at their college, we need to know how
large a sample is necessary to make an accurate estimate.
It depends on three things
1. What is the maximum amount of error you want to have (i.e. how
close to the true mean do you want to be? 2 years, 5 years, etc)
2. What is the standard deviation (which you will always be given)
3. What is the degree of confidence (i.e. 90%, 95%, or 99%)
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7.2b Find sample size.notebook
April 19, 2018
Formula for Determining the Best Sample Size
The formula for determining our confidence interval, gives us a
formula for Maximum error.
So
E = max error
Max error
•
If we take the formula for max error:
N=
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7.2b Find sample size.notebook
April 19, 2018
The college president asks the statistics teacher to estimate the
average age of the students at their college. How large a sample is
necessary? The statistics teacher would like to be 99% confident
that the estimate be accurate within 1 year. From a previous study,
the standard deviation of the ages is known to be 3 years
n=
( z X σ )2
E
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7.2b Find sample size.notebook
April 19, 2018
A company has a new diet pill. The company would like to be 95%
accurate in their average weight lose claims, within 2 pounds. The
standard deviation is known to be 3 pounds. How large a sample
should the company survey?
n=
( z X σ )2
E
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7.2b Find sample size.notebook
April 19, 2018
Find the minimum sample size needed to estimate a
population mean if the population standard deviation is
24, the confidence interval desired is 90%, and a
maximum error of the estimate is 5.
n=
(z X σ )2
E
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7.2b Find sample size.notebook
April 19, 2018
pg 337 19­25
19. Noise levels at various urban hospitals were measured in decibels. The mean of
the noise levels in 84 corridors was 61.2 decibels, and the standard deviation was
7.9. Find a 95% confidence interval of the true mean.
20. The growing season for a random sample of 35 cities were recorded, yielding a
sample mean of 190.7 days and a sample standard deviation of 54.2 days.
Estimate the true mean population of the growing season with a 95% confidence.
21. How many cities growing season would need to be sampled in order to estimate
the true mean growing season with 95% confidence within an error of 2 days.
Sample standard deviation of 54.2 days.
22. In hospital study cited in Problem 19, the mean noise level is 171 corridors was
58db and the standard deviation was 4.8db. Find a 90% confidence interval of the
true mean.
23. An insurance company is trying to estimate the average number of sick days
that an employee uses per year. A pilot study found the standard deviation is 2.5
days. How large of sample is needed if the company wants to be 95% confident of
getting an interval of the true mean with a maximum error of 1 day?
24. A restaurant wants to have a 99% confidence interval of the true mean cost of a
dry martini. How large of a sample is needed if he wishes to be accurate with
$0.10? Standard deviation of $0.12.
25. A nurse wants to estimate the birth weight of infants. How large of a sample is
needed if she wants a 90% confident that the true mean is within 6 ounces of the
sample mean? Standard deviation of 8 ounces.
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