Notes regarding Two-Sample t-Tests and ANOVAs
In Chapter 9, we learned how to conduct a t test of a hypothesis when we were testing the mean of a single sample group against some pre-determined value (i.e., the 21.6 gallons of milk consumption as the national average). This week, in Chapter 10, we will see how to test hypotheses that involve more than one sample group—such as testing to see if males are significantly taller than females. If we have two groups, then the technique that we will use will still be a t test. If we have more than two groups, then we will have to use a different test called Analysis of Variance (ANOVA, for short).
The good news is that the ...view middle of the document...
e., click Data along the top menu and then you should see the Data Analysis option to the right). If you click on Data Analysis and then scroll down to the t-test options (they are in alphabetical order), you will see that there are three different types of t tests that Excel can perform. For purposes of this course, we will not be using the t-Test: Two Sample Assuming Unequal Variances, so you will not need to worry about that one. We will use t-Test: Two Sample Assuming Equal Variances whenever we have two completely separate groups (i.e., males and females, college students and high school students, etc.) for which we have data. We will use t-Test: Paired Two Sample for Means (a paired sample t test) whenever we have one group of subjects for which we have two separate observations, such as a before and after test for a weight loss program—it would be the same participants and we would measure their weight twice, once before the program and again after the program.
Let’s consider the example data at the top of page 432. A company is considering adopting a new software system, but they want to make sure that it will work more quickly than their current system. A sample was set up where the current software was used and the time taken to complete the project was measured for one group and then for a second group, the new software was used and the time taken to complete the project was measured. This is going to be a t-Test: Two Sample Assuming Equal Variances because we have two completely separate groups (those using the current software and those using the new software).
Before we conduct a hypothesis test, we need to state our hypotheses, so that we know what we are testing. Since the company wants to see if the new software is quicker, our hypotheses would be:
H0: µC ≤ µN
Ha: µC > µN
In this case, µN stands for the mean time to complete using the new software and µC stands for the mean time to complete using the current software. In our alternative hypothesis, we are speculating that the current software would take a longer mean time as compared with the new software. Just like last week, since the alternative hypotheses contains > (as opposed to ≠), this is a one-tailed test.
To conduct our test, we first have to enter the data, then we go to the Data Ribbon and select Data Analysis. Within the popup box, we choose t-Test: Two Sample Assuming Equal Variances and we should get a popup box that looks like this:
In the box for Variable 1 Range, we select the data for the current software (including the column label), A1:A13. In the box for Variable 2 Range, we select the data for the new software, B1:B13. Since we included the labels within our data ranges (we’ll see why in a minute), we need to check the Labels box. Note that Alpha is already set to 0.05. If the problem tells us to use a different alpha, then we would change that, but we will virtually always use alpha = .05 (95% confidence) in...