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 0.05 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	82	80
2	85	88
3	89	83
4	90	90
5	97	93
6	102	100
7	103	103
8	108	107
9	112	106
10	119	111

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 two-tailed test. This is a left-tailed test.     This is a right-tailed test.

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

_d

=

(c) What is 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 their younger sibling. There is not enough data to support the claim that, on average, older siblings have a higher IQ than their younger sibling.     We reject the claim that, on average, older siblings have a higher IQ than their younger sibling. We have proven that, on average, older siblings have a higher IQ than their younger sibling.

Answer 1

a) This is a paired sample T test, as the pair in comparison are siblings. This is a right-tailed test.

option b, c & d is covered in the solution below.)

d) reject H₀

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