Transcript 38. COMPUTING FOR THE SAMPLE SIZE TO ESTIMATE

ESTIMATING
APPROPRIATE SAMPLE
SIZE
Determining sample Size
z*
σ
√n
≤m
How Many monkeys?
Researchers would like to estimate the mean
cholesterol level ℳ of a particular variety of
monkey that is often used in laboratory
experiments. They would like their estimate to be
within 1mg/dl of blood of the true value of ℳ at
95% confidence level. A previous study involving
this variety of monkeys suggests that the sd of
cholesterol level is about σ = 5mg/dl. Obtaining
monkeys is time consuming and expensive so
the researchers want to know the minimum
number of monkeys they will need to generate a
satisfactory estimate.
CI: 95%
z* = 1.96
σ= 5mg/dl
1.96
5
z*
√n
≤m
≤1
√n
√n
σ
≧
(1.96) (5)
1
√n
≧
9.8
n
≧
96.04
Researchers would
need 97 monkeys
to estimate the
cholesterol levels
to their satisfaction.
z*
σ
√n
≤E
E = maximum error of estimate
Finding the appropriate
sample size (n)
Mr. Delton asks Charlii to estimate the average age
of the students in BHS. Mr. Delton is confident that
Charlii will be able to find the minimum number of
students he needs for his estimate to be reliable.
Charlii would like to be 99% confident that the
estimate should be accurate within 1 year. From a
previous study, the standard deviation of the ages is
known to be 3 years.
∂ = 3 years
E = 1 year
Z* = 2.58
∂ = 3 years
E = 1 year
z*
n ≥ 59.9
σ
√n
Z* = 2.58
≤E
Therefore, Charlii needs to have at least
60 students to be 99% confident that the
estimate is within 1 year of the true
mean age of the students in BHS
Your Turn!
A restaurant owner wishes to find 99%
confidence interval of the true mean
cost of a dry martini. How large should
the sample be if she wishes to be
accurate within $0.10? A previous
study showed that the population
standard deviation of the the price was
$0.12.
Facts about the margin of
error
z* gets smaller. The trade-off: to obtain smaller
margin of error from the same data, you must be
willing to accept lower confidence.
σ gets smaller: its easier to pin down ℳ when σ
is small
n gets bigger: increasing the sample size reduces
the margin of error. To cut the margin of error in
half, you must take four times as many
observations from the population.