One hundred teachers attended a seminar on mathematical problem solving. The att

Question

One hundred teachers attended a seminar on mathematical problem solving. The attitudes of representative sample of 12 of the teachers were measured before and after the seminar. A positive number for change in attitude indicates that a teacher's attitude toward math became more positive. The twelve change scores are as follows. 4; 8; - 1; 1; 0; 5; - 3; 2; - 1; 6; 5; - 2 What is the mean change score? What is the standard deviation for this sample? What is the median change score? Find the change score that is 2.2 standard deviations below the mean.

Explanation / Answer

By using R -software

(a) to (c) command are as follows

x=c(4,8,-1,1,0,5,-3,2,-1,6,5,-2)
x
n=length(x)
n
mean(x)
s=var(x);s
var=((n-1)/n)*s
var
sd=sqrt(var)
sd
median=median(x)
median

Output

> x=c(4,8,-1,1,0,5,-3,2,-1,6,5,-2)
> x
[1] 4 8 -1 1 0 5 -3 2 -1 6 5 -2
> n=length(x)
> n
[1] 12

#(a)

> mean(x)
[1] 2

(b)
> s=var(x);s
[1] 12.54545
> var=((n-1)/n)*s
> var
[1] 11.5
> sd=sqrt(var)
> sd
[1] 3.391165

#The standard deviation of this sample is 3.39.

#(c)

> median=median(x)
> median
[1] 1.5

The median change score is 1.5.

#(d)The change score
= 2 - 2.2*3.39
= 2-7.458
= -5.458

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