Question

Sibling IQ Scores: 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, on average, older siblings have a higher IQ than their younger sibling. The results are depicted for a sample of 10 siblings in the table below. Test the claim at the 0.01significance level. You may assume the sample of differences comes from a normally distributed population.

Pair ID	Older Sibling IQ (x)	Younger Sibling IQ(y)	difference (d = x − y)
1	86	82	4
2	89	94	-5
3	93	87	6
4	94	94	0
5	101	97	4
6	106	104	2
7	107	107	0
8	112	111	1
9	116	110	6
10	123	115	8
Mean	102.7	100.1	2.6
s	12.2	11.0	3.8

If you are using software, you should be able copy and paste the data directly into your software program.

(a) What is the test statistic? Round your answer to 2 decimal places.

t_d =  
To account for hand calculations -vs- software, your answer must be within 0.01 of the true answer.

(b) Use software to get the P-value of the test statistic. Round to 4 decimal places.
P-value =  

(c) What is the conclusion regarding the null hypothesis?

reject H₀

fail to reject H₀    
(d) Choose the appropriate concluding statement.

The data supports the claim that, on average, older siblings have a higher IQ than younger siblings.

There is not enough data to support the claim that, on average, older siblings have a higher IQ than younger siblings.    

We reject the claim that, on average, older siblings have a higher IQ than younger siblings.

We have proven that, on average, older siblings have a higher IQ than younger siblings.

Answer 1

Number	Before	After	Difference
	86	82	4	1.96
	89	94	-5	57.76
	93	87	6	11.56
	94	94	0	6.76
	101	97	4	1.96
	106	104	2	0.36
	107	107	0	6.76
	112	111	1	2.56
	116	110	6	11.56
	123	115	8	29.16
Total	1027	1001	26	130.4

To Test :-

H0 :-  

H1 :-

Test Statistic :-





t = 2.16

Test Criteria :-
Reject null hypothesis if


Result :- Fail to reject null hypothesis

Decision based on P value
P - value = P ( t > 2.16 ) = 0.0295
Reject null hypothesis if P value < level of significance
P - value = 0.0295 > 0.01 ,hence we fail to reject null hypothesis
Conclusion :- Fail to reject null hypothesis

There is not enough data to support the claim that, on average, older siblings have a higher IQ than younger siblings.