Question

Then you will do a paired t-test on the two # of letters variables using a level of significance. What is the test-statistic and p-value?

# of letters in first name	#letters in last name
5	6
5	5
7	7
4	6
7	7
6	5
7	9
6	9
4	12
5	7
4	5
7	5

Answer 1

The following table is obtained:

	Sample 1	Sample 2	Difference = Sample 1 - Sample 2
	5	6	-1
	5	5	0
	7	7	0
	4	6	-2
	7	7	0
	6	5	1
	7	9	-2
	6	9	-3
	4	12	-8
	5	7	-2
	4	5	-1
	7	5	2
Average	5.583	6.917	-1.333
St. Dev.	1.24	2.151	2.535
n	12	12	12

and the sample size is n = 12. For the score differences we have

Test Statistics

The t-statistic is computed as shown in the following formula:

Using the P-value approach: The p-value is p = 0.0957