# Help

#### 1NAMILL

##### New Member
I need some assistance with the following 2 questions:

Question 1:

Assume that you want to test the claim that the paired sample data come from a population for which the mean difference is = 0. Compute the value of the t test statistic.

x 7 2 7 3 10
y 4 4 3 4 5

Use three decimal places.

This is what I did:

Mean = 1.8
Standard Deviation = 4.069
Sqrt of n (5) = 2.236

By using the Studen t distribution I calculated the following:

t = mean of the difference - 0/sd/sqrt of n

t = 1.8-0/4.069/2.236 = 1.8/1.8197 = 0.989

This answer is incorrect. What am I missing?

#### JohnM

##### TS Contributor
The standard deviation of the differences should be 3.114.

#### 1NAMILL

##### New Member
How did you get 3.114? I must have did something wrong. Can you walk me through the standard deviation process for the above problem requested?

#### JohnM

##### TS Contributor
For the x and y sets, d = x-y:

3, -2, 4, -1, 5

the mean of d is 1.8

the std dev is the square root of the sum of squared differences (x-mu)^2 divided by n-1

(3-1.8)^2 = 1.44
(-2-1.8)^2 = 14.44
(4-1.8)^2 = 4.84
(-1-1.8)^2 = 7.84
(5-1.8)^2 = 10.24

= sqrt(38.8/4) = sqrt(9.7) = 3.114