I A researcher suspects that studying with music playing in the background signi
ID: 3368365 • Letter: I
Question
I A researcher suspects that studying with music playing in the background significantly reduces the amount of information that is retained. She conducted a study in which 18 participants were randomly assigned to either a music study group (n-9) or a quiet study group (n-9) and provided with the same list of words to memorize for the same amount of time. The music study group listened to a popular radio station while studying and the quiet group studied with no noise. Both groups were tested on their ability to recall the words from the study list. The data were normally distributed and were as follows: Music group Quiet group 5 4 10 5 4. 7 7Explanation / Answer
A) The best test for use is equality of population mean(t-test).
B) The hypothesis are:
let u1= average of recall words in music group.
u2= average of recall words in Quiet group.
H0 : u1=u2
Ha : u1>u2 or u1<u2
C) The r code for t-test is:
x=c(5,4,5,4,6,3,7,7,5)
y=c(11,10,9,7,8,7,8,9,9)
t.test(x,y)
And the output is:
> t.test(x,y)
Welch Two Sample t-test
data: x and y
t = -5.6132, df = 15.985, p-value = 3.9e-05
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-4.898472 -2.212639
sample estimates:
mean of x mean of y
5.111111 8.666667
Here |t| observed is 5.6132 . and The table value of |t (16,0.025)| is 2.11995.
D) Here obs. |t| > Table |t| . Thus we reject H0 at 5% l.o.s.
E) And conclude that there is significant difference in average of recall words in music group and average of recall words in Quiet group.
F) The effect size is given as below:(By using R-code)
x=c(5,4,5,4,6,3,7,7,5)
y=c(11,10,9,7,8,7,8,9,9)
n1=length(x);n2=length(y)
effectsize=abs((mean(x)-mean(y)))/(sqrt(((n1-1)*var(x)+(n2-1)*var(y))/(n1+n2-2)))
effectsize
And the output is :
> effectsize
[1] 2.646074
Thus the effect size is 2.646074.
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