Question

Sibling IQ Scores (Raw Data, Software Required):
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 0.01 significance level. You may assume the sample of differences comes from a normally distributed population.

Pair ID	Older Sibling IQ (x)	Younger Sibling IQ(y)
1	85	81
2	88	93
3	92	86
4	93	93
5	100	96
6	105	103
7	106	106
8	111	110
9	115	109
10	122	114

You should be able copy and paste the data directly into your software program.

(a) The claim is that the mean difference (x - y) is positive (μ_d > 0). What type of test is this?

This is a left-tailed test.

This is a two-tailed test.    

This is a right-tailed test.

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

(c) What is the P-value of the test statistic? Round to 4 decimal places.

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

reject H₀

fail to reject H₀    

(e) Choose the appropriate concluding statement.

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

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

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

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

Answer 1

The table given below ,

Pair ID	Older Sibling IQ (X)	Younger Sibling IQ (Y)	di=X-Y	di^2
1	85	81	4	16
2	88	93	-5	25
3	92	86	6	36
4	93	93	0	0
5	100	96	4	16
6	105	103	2	4
7	106	106	0	0
8	111	110	1	1
9	115	109	6	36
10	122	114	8	64
		Sum	26	198

From table,

Let ,

(a) Hypothesis : Vs

This test is a right-tailed test.

(b) The test statistic is ,

(c) p-value = ; From excel "=TDIST(2.16,9,1)"

(d) Decision : Here , p-value=0.0295 >

Therefore , Fail to reject Ho.

(e) Conclusion :

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