Question

(6 pts) Ten randomly selected people took an IQ test A, and next day they took a very similar IQ test B. Their scores are shown in the table below.

Person	A	B	C	D	E	F	G	H	I	J
Test A	104	90	109	73	118	81	93	130	108	100
Test B	104	90	109	75	119	81	92	129	108	104

1. Consider (Test A - Test B). Use a 0.05 significance level to test the claim that people do better on the second test than they do on the first. (Note: You may wish to use software.)

(a) What test method should be used?

A. Two Sample z
B. Matched Pairs
C. Two Sample t

(b) The test statistic is:

(c) The critical value is:

(d) Is there sufficient evidence to support the claim that people do better on the second test?

A. No
B. Yes


2. Construct a 95% confidence interval for the mean of the differences. Again, use (Test A - Test B).
____ < μ < ____

THANK YOU!!!!

Answer 1

Matched pair test is used when there are two treatments ( Test A and B) and test subjects are paired and each subject in a pair is assigned to a treatment randomly. In our scenario, the same test subject is subject to the two treatments one on 1st day and the other on the 2nd day.

H_o:

H_a:

Person	Test A	Test B	Diff
A	104	104	0
B	90	90	0
C	109	109	0
D	73	75	-2
E	118	119	-1
F	81	81	0
G	93	92	1
H	130	129	1
I	108	108	0
J	100	104	-4
Mean	100.600	101.100	-0.500
		Variance	2.278

Standard error =

At 5% significance, the t statistic is very low to conclude that people do better on the second test.

95% confidence interval: ​​​​​​​