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EXERCISES 191
2. Estimates of may be available from previous or similar studies.
3. If it is thought that the population from which the sample is to be drawn is approximately
normally distributed, one may use the fact that the range is approximately
equal to six standard deviations and compute s L R>6. This method
requires some knowledge of the smallest and largest value of the variable in the
population.
EXAMPLE 6.7.1
s 2
A health department nutritionist, wishing to conduct a survey among a population of
teenage girls to determine their average daily protein intake (measured in grams), is seeking
the advice of a biostatistician relative to the sample size that should be taken.
What procedure does the biostatistician follow in providing assistance to the nutritionist
Before the statistician can be of help to the nutritionist, the latter must provide
three items of information: (1) the desired width of the confidence interval, (2) the level
of confidence desired, and (3) the magnitude of the population variance.
Solution:
Let us assume that the nutritionist would like an interval about 10 grams
wide; that is, the estimate should be within about 5 grams of the population
mean in either direction. In other words, a margin of error of 5 grams
is desired. Let us also assume that a confidence coefficient of .95 is decided
on and that, from past experience, the nutritionist feels that the population
standard deviation is probably about 20 grams. The statistician now has the
necessary information to compute the sample size: z = 1.96, s = 20, and
d = 5. Let us assume that the population of interest is large so that the statistician
may ignore the finite population correction and use Equation 6.7.3.
On making proper substitutions, the value of n is found to be
n = 11.9622 1202 2
152 2
= 61.47
The nutritionist is advised to take a sample of size 62. When calculating
a sample size by Equation 6.7.3 or Equation 6.7.5, we round up
to the next-largest whole number if the calculations yield a number that
is not itself an integer.
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EXERCISES
6.7.1 A hospital administrator wishes to estimate the mean weight of babies born in her hospital. How
large a sample of birth records should be taken if she wants a 99 percent confidence interval that
is 1 pound wide Assume that a reasonable estimate of s is 1 pound. What sample size is required
if the confidence coefficient is lowered to .95
6.7.2 The director of the rabies control section in a city health department wishes to draw a sample from
the department’s records of dog bites reported during the past year in order to estimate the mean