Question

There have been numerous studies involving the correlation and differences in IQ's among siblings. Here we consider a small example of such a study. We will test the claim that older siblings have a higher IQ than younger siblings. The results are depicted for a sample of 10 brothers in the table below.

	IQ score										mean	?s
Older brother (?x)	106	117	107	106	99	101	79	92	107	86	100	11.3627070327062
Younger brother (?y)	109	115	104	95	89	92	80	92	97	87	96	10.6144555520604
?=?−?d=x−y	-3	2	3	11	10	9	-1	0	10	-1	4	5.43650214343336

(a) Find the test statistic.

(b) Test the claim at the 0.01 significance level.

Critical value:

Is there sufficient data to support the claim?
Yes
No

(c) Test the claim at the 0.05 significance level.

Critical value:

Is there sufficient data to support the claim?
Yes
No

Answer 1