Let’s work a sample size problem.
A random sample size, n, is to be taken from a large population having a standard deviation of 1″. The sample size is to be determined so that there well be a 0.05 risk probability of exceeding a 0.1″ tolerance error in using the sample mean to estimate μ. Which of the following values is nearest the required sample size?
a. 42
b. 106
c. 203
d. 384
Please work out your answer, add a comment with your result and show your work, please. Don’t peek at the comments if you’ve not worked it yet.
[note to self: find a way to use a multiple choice feature that tallies the results]
This problem from the Quality Council of Indiana with permission.
Related:
Sample Size – success testing (article)
Sample size (article)
Hypothesis Test Sample Size (article)
n = ( z^2 * σ^2 ) / ME^2
To find z:
the cumulative probability is 1 – alpha/2 = 1 – 0.05/2 = 0.975
from z table, for 0.97 z=1.96
ME = 0.1″
σ = 1
so, n = ( 1.96^2 * 1^2 ) / 0.1^2 = 384.16
So, correct answer is D.
Thanks for the question Fred.
Correct – I found that having the most common values of the z-table ready to go, did save time. Alpha of .01, .05, .1 for example. And, knowing how to use the table for that question that was for alpha of .03 for some reason.