Effect of sample size on sampling error
The larger the sample size, the smaller the sampling error. However when the population is large, sampling a small proportion of the population may still give accurate estimates.
Sampling error depends much more strongly on the sample size than on the proportion of the population that is sampled.
For example, a sample of 10 from a population of 10,000 people will estimate the proportion of males almost as accurately as a sample of size 10 from a population of 100.
The cost savings from using a sample instead of a full census can be huge.
Shelving for large library books
The manager of a library intends to purchase new shelving for its collection and wonders what proportion of its books will fit on shelves with 'standard' spacing. Since there are over one million books in the library, it is infeasible to classify all books as normal or outsize, so the decision on shelving must be made from a sample of books.
To investigate how many books must be sampled, we will sample from a population of 1,000,000 books in which 20% are outsize.
Initially we will take random samples of 1,000 books. Click Take sample a few times. The difference between the sample proportion of outsize books and the population proportion (0.200) is the sampling error.
Use the pop-up menu to investigate how the sample size affects the accuracy of the estimate. You should observe that the sampling error is usually smaller when the sample size is large.
In practice, a sample size of 1000 books would give the library a sufficiently accurate estimate of the proportion of outsize books. It is certainly hard to imagine a situation where more than 1% of this population would need to be sampled!