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	83	79
2	86	89
3	90	86
4	91	91
5	98	94
6	103	101
7	104	104
8	109	108
9	113	107
10	120	112

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

The statistical software output for this problem is:

Hence,

a) This is a right tailed test.

b) Test statistic = 2.54

c) P - value = 0.0159

d) Reject Ho

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