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 0.01 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) difference (d = x − y)

Pair ID	Older Sibling IQ (x)	Younger Sibling IQ(y)	difference (d = x − y)
1	83	81	2
2	86	91	-5
3	90	86	4
4	91	91	0
5	98	94	4
6	103	101	2
7	104	104	0
8	109	108	1
9	113	107	6
10	120	112	8
Mean	99.7	97.5	2.2
s	12.2	10.4	3.6

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

This is a right-tailed test.

This is a left-tailed test.

This is a two-tailed test. (

b) 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 0.012 of the true answer.

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

(d) What is the conclusion regarding the null hypothesis? reject H0 fail to reject H0

(e) 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

The statistical software output for this problem is:

Paired T hypothesis test: HD = 11 - 12 : Mean of the difference between Older Sibling IQ (x) and Younger sibling IQ(Y) Ho : D = 0 HA: WD > 0 Hypothesis test results: Difference Mean Std. Err. DF T-Stat P-value Older Sibling IQ (x) - Younger sibling IQ(y) 2.2 1.1430952 91.9245991 0.0432

Hence,

a) Right - Tailed Test

b) Test statistic = 1.92

c) P - value = 0.0432

d) Fail to reject Ho

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