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 (μd > 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.

Td =

(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 right tailed test. Since the claim is whether the mean difference is positive or not.

Hypothesis:

• Null: The mean difference .
• Alternative: The mean difference .

R Code and Output:

b)

The test statistic t = 0.50

c)

The p-value of the test statistic is 0.6215

d)

Since the p-value is 0.6215 > 0.05 we fail to reject the Null Hypothesis H0. So, The mean difference .

e)

Concluding Statement:

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