Determining Sample Sizes for the Purpose of Estimation
Survey Sampling Examples 1-2 were designed to challenge your ability to estimate
means within 95% confidence.
The current exercise was developed to challenge your ability to determine what the
sample size would be in both examples given a bound and estimate of population
variance.
Mean Estimation for a Simple Random Sample
Example 1: N = 1,850, a 5 point Likert item is used.
Problem 1 Assume that a population variance of .2 has been obtained, and that the
board members want a bound of + .10.
Problem 2 Assume that the board members want a bound of + .05, and that you
have no estimate of population variance (use Tchebysheff's theorem for a
5 point Likert item).
Problem 3 Assume that a population standard deviation of .4 has been obtained,
and that the board members want a bound of + .07.
Example 2: N = 20,000, a 10-item questionnaire is used (each item scaled 1 to 5) for
the purpose of producing satisfaction scores ranging from 10 to 50.
Problem 4 Assume that a population standard deviation of 8 has been obtained, and
that the financial aid department wants a bound of + 5 points.
Problem 5 Assume that financial aid department wants a bound of + 2 points
around the mean score, and that you have no estimate of population
variance (use Tchebysheff's theorem).
Problem 6 Assume that a population variance of 49 has been obtained, and that the
financial aid department wants to assume a standard error of 2.0.
Further assume that financial aid department wants to be roughly 95%
confident in its estimate.
Proportion Estimation for a Simple Random Sample
Example 3: A University president wants to conduct a simple random sample of
college students to determine the proportion of students in favor of converting the
semester system to the quarter system. How many students should she have
interviewed? (Assume N = 2000 and a desired bound of .02). Use the maximum
variance possible for a proportion in the population.
Mean Estimation for a Stratified Random Sample
Example 4: A school desires to estimate the average score that may be obtained on
a reading comprehension exam for students in the sixth grade. The school’s
students are grouped into three tracks, with the fast learners in track I and slow
learners in track III. The school decides to stratify on tracks since this method
would reduce the variability of test scores. The sixth grade contains 55 students in
track I, 80 students in track II, and 65 students in track III. A stratified random
sample of students, proportionately allocated, is desired. Assuming a bound of .05
and prior evidence that the scores have a variance of 10, determine what sample
size is needed.