Question

A researcher predicts that students will learn most effectively with a constant background sound, as opposed to an unpredictable sound or no sound at all. For group 1 subjects study with background sound at a constant volume in the background. For group 2 subjects study with noise that changes volume periodically. For group 3 subjects study with no sound at all. After studying, students take 10 point multiple choice test over the material. Their scores follow:

Constant Sound	Random Sound	No Sound
7	5	2
4	5	2
6	3	3
8	4	1
6	4	2
6	7	1
2	2	4
9	2	4

What is the test statistics of the above data analysis if the three groups are independent groups?

What is the p-value of the above analysis?

Which of the following statement is correct:

Select one:

a. There were significant differences between for all different sound conditions.

b. The subjects’ score of constand background sound is significantly higher than that of the random background sound condition.

c. The subjects’ score of random backgroundsound is significantly higher than that of the no background sound condition.

d. The subjects’ score of constant background soud is significantly higher than that of the no background sound condition.

What if the three conditions were given to one group of subjects only? What would be the test statistics?

What would be the p-value?

The parametric assuption of the data is assumed.

Select one:

a, True

b, False

Answer 1

Ho: µ1=µ2=µ3
H1: not all means are equal

treatment	Constant Sound	Random Sound	No Sound
count, ni =	8	8	8
mean , x̅ i =	6.000	4.00	2.375
std. dev., si =	2.204	1.690	1.188
sample variances, si^2 =	4.857	2.857	1.411
total sum	48	32	19		99	(grand sum)
grand mean , x̅̅ =	Σni*x̅i/Σni =	4.13
square of deviation of sample mean from grand mean,( x̅ - x̅̅)²	3.516	0.016	3.063
					TOTAL
SS(between)= SSB = Σn( x̅ - x̅̅)² =	28.125	0.125	24.500		52.75
SS(within ) = SSW = Σ(n-1)s² =	34.000	20.000	9.875		63.8750

no. of treatment , k =   3
df between = k-1 =    2
N = Σn =   24
df within = N-k =   21
  
mean square between groups , MSB = SSB/k-1 =    26.3750
  
mean square within groups , MSW = SSW/N-k =    3.0417
  
F-stat = MSB/MSW =    8.6712

value of test stat=   8.67
p value is    0.0018
  
a. There were significant differences between for all different sound conditions.