Answer:
It is statistically significant that mean of difference scores is different from 0
Step-by-step explanation:
Subject Bar 1 Bar 2 Difference
1 20 40 20
2 18 25 7
3 24 38 14
4 14 27 13
5 5 31 29
6 26 21 -5
7 15 32 17
8 29 38 9
9 15 25 10
10 9 18 9
Mean of difference =[tex]\frac{Sum}{10}=\frac{123}{10}=12.3[/tex]
Standard deviation s =[tex]\sqrt{\frac{(x_i-\bar{x})^2}{n}}=8.93[/tex]
Null Hypothesis : mean of difference scores is 0 : [tex]H_0:\mu=0[/tex]
Alternate Hypothesis : mean of difference scores is different from 0 : [tex]H_a:\mu \neq 0[/tex]
We will use t test for unpaired
[tex]t = \frac{x-\mu}{\sqrt{\frac{s^2}{n-1}}}\\t = \frac{12.3-0}{\sqrt{\frac{8.93^2}{10-1}}}\\t=4.13[/tex]
Level of significance (two tailed) =[tex]\alpha = 0.05[/tex]
Degree of freedom = n-1 = 10-1 =9
Using calculator
The p-value is .002559.
p value < α
So ,we reject null hypothesis
So, It is statistically significant that mean of difference scores is different from 0