Merlot Assignment – Project Synergy  

Making Inferences about Two Means for Independent and Small Samples

By Angela Walters – Capitol College

 

Course: Any class involving elementary statistics concepts.  

Uses the Merlot website ‘Student’s t-test (Statistics)’ by Bryan Lewis  

Background: The t-test is used to compare the means of two populations when the number of sample values is 30 or fewer. When performing a hypothesis test on two samples with sample size less than 30 the student t distribution is used to determine the test statistic and critical values. For an essentially normally distributed population the student t distribution for samples of size n has the form: , where s = sample standard deviation; = sample mean; = the population mean.

 

Since we are looking at small samples where the population standard deviation is not known we need to make some the assumptions need to be made. We will assume the samples are random samples, and that the starting population is essentially normal.

 

Assignment:  

1. Given the following two sets of  IQ scores.  

I: 105  102  103  104  114  104  114   102  123  123  114  124  114  114  115  120  110

II: 97  99  100  99  101  111  106  107  110  110  99  113  123  109  110  118

  2. Go to the site http://nimitz.mcs.kent.edu/~blewis/stat/scon.html and select the student’s t-test applet link. Enter the above sets of data in the ‘data’ window. Select the compute button.

  3. To test the claim that the IQ scores come from populations with the same mean, scroll down the ‘analysis’ window to view the results. Record the results along with the test statistic and p-value values used to find the results.

  4.    If this experiment is repeated 10 times, what would be the number of times you will  conclude the two population means are different? How does this relate to a type one error?