Question B 03
A researcher measures the length of 16 adult wombats and finds a sample mean of 57 cm and a sample standard deviation of 12 cm. The standard error of the mean is estimated to be 3 cm. If she plans to carry out measurements on 100 more wombats, the following can be expected (place an X in exactly one column for each row):
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!
Each row of the table can be stated as its own question, most of which can be determined through common sense:
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.
Let us consider each row of the table:
The sample mean should stay roughly the same. This is because the mean length of adult wombats is a well-defined quantity, and we have no information to suggest that we have been sampling adult wombat length in a biased manner.
The sample maximum is likely to increase. This is simply because the larger the set sampled, the more likely you are to include extreme outliers, which will increase the maximum and decrease the minimum of your set. In more technical notation, this is the same as saying when B is a subset of A.
The standard error of the mean will decrease. Recall that the standard error of the mean estimates how far away your sample mean is from the "true" population mean. More and more samples will improve the accuracy of your sample mean, decreasing the error. This can also be seen in the formula for standard error of the mean:
where s is the standard deviation of the sample and n is the number of objects sampled. As n increases, the overall fraction will decrease.
So the table should be filled in as follows: