An investigation of the effectiveness of a training program to improve customer relationships included a pre-training and post-training customer survey. To compare the differences they computed (post-training survey score - pre-training survey score). Seven customers were randomly selected and completed both surveys. The results follow: Customer Pre-training Survey Post-training Survey
A 6 8
B 5 5
C 10 10
D 7 10
E 6 8
F 5 6
G 2 8

What is the value of the test statistic?
a. 1.943
b. 1.895
c. 2.542
d. 2.447

2.542

Step-by-step explanation:

Given the data :

Customer Pre-training Survey, x1 __Post-training Survey, x2 __ difference, d = (x2-x1)

A 6 8 2

B 5 5 0

C 10 10 0

D 7 10 3

E 6 8 2

F 5 6 1

G 2 8 6

This is a paired test as each subject has two different data values :

Difference in score, d :

dbar = Σd / n

dbar = (2+0+0+3+2+1+6) /

dbar = 14 / 7

dbar = 2

Standard deviation of d ; Sd = √[Σ(d - dbar)²/n-1]

Using calculator ; Sd = 2.082

Test statistic = dbar ÷ (Sd/√n)

Test statistic = 2 ÷ (2.082 / 7)

Test statistic = 2 ÷ 0.7869220

The statistic = 2.5415

10

step-by-step explanation:

7+3=10

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation: