Research Methods 2

Topic 6: Introduction to Standard Errors
(Week 6)

Aims

To understand that how good a sample mean is as an estimate of the population mean depends on sample size.  Also to understand how this idea might be quantified.

To be able to explain what the distribution of a sample mean is and to explain qualitatively how it changes with the size of the sample.

To understand how the precision with which a sample mean estimates a population mean can be quantified by measuring the spread of the distribution of sample means, using a collection of many samples.

To know that the SD of the distribution of sample means is called the Standard Error (SE) and that this is an appropriate measure of precision of the sample mean

To know the correct formula for estimating a standard error from a single sample.

This week there is only one document to be studied and one exercise sheet.  You will be studying the issue of how well a sample mean performs as an estimator of the population mean and seeing how this is affected by sample size.  You will also study how the standard error quantifies this aspect of a sample mean and how to calculate it.

• Study the document How good is my estimate? The meaning of Standard Errors, which explains the ideas behind the standard error.
• Answer the questions in Exercise Sheet 1.

{note that you will need to download a Minitab macro for question 3 and another for question 5.  To learn what Minitab macros are, where you should save them and how to use the macro needed for question 3, click here.  You can obtain the  macro for question 3 by right-clicking here and choosing 'Save Target As...'*.  The description of the macro needed for question 5 is given here and the macro itself can be obtained by right-clicking here and choosing 'Save Target As...'.}
* this is what you do in Internet Explorer - with other browsers choose an equivalent function to download the file.  Also, when the dialogue box for the location for saving the file comes up, there may be an option 'Save as type'.  If the default is 'Text file', change this to 'All files' before downloading.
 
• You should check your answers by referring to the Solutions to Exercise Sheet 1.

There is no formal assessment this week.