Question

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	108	114	127	110	101	77	99	96	82	89
Test B	109	115	127	115	105	75	101	100	85	91

Consider (Test A - Test B). Use a 0.01 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. Matched Pairs B. Two Sample z 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 99 % confidence interval for the mean of the differences. Again, use (Test A - Test B). ____ <?< ____

Answer 1

a) Matched pair t test because conducted tests on same people in day1 and day2

Hypothesis:

Ho: μD​ ≥ 0

Ha: μD​ < 0

Test:

	Test A	Test B	A-B
	108	109	-1
	114	115	-1
	127	127	0
	110	115	-5
	101	105	-4
	77	75	2
	99	101	-2
	96	100	-4
	82	85	-3
	89	91	-2
Mean	100.3	102.3	-2
Sd	15.20270444	15.50662941	2.108185107
n	10	10	10
b) t stat	-3	Mean/(Sd/SQRT(n))
c) t critical	-2.82143793	T.INV(0.01,9)	Left tailed
P value	0.007478182	T.DIST(ts,df,TRUE)
t stat	<	t critical	Reject H0
P value	<	0.01	Reject H0

d) Conclusion:

Yes, there is sufficient evidence to support the claim that people do better on the second test

e) 99% CI:

99% CI	tc	3.249835542	T.INV.2T(0.01,9)	Two tailed
Lower	-4.16655703	Mean+tc*Sd/SQRT(n)
Upper	0.166557028	Mean-tc*Sd/SQRT(n)

CI = (-4.1665, 0.1666)