Sibling IQ Scores (Raw Data, Software Required): There have been numerous studie

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.

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 (d > 0). What type of test is this?

This is a left-tailed test.

This is a right-tailed test.    

This is a two-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.

Pair ID Older Sibling IQ (x) Younger Sibling IQ(y) 1 85 81 2 88 91 3 92 88 4 93 93 5 100 96 6 105 103 7 106 106 8 111 110 9 115 109 10 122 114

Explanation / Answer

The statistical software output for this problem is:

Paired T hypothesis test:
D = 1 - 2 : Mean of the difference between Older Sibling IQ (x) and Younger sibling IQ (y)
H0 : D = 0
HA : D > 0
Hypothesis test results:

Hence,

a) This is a right-tailed test.

Option B is correct.

b) Test statistic = 2.54

c) p - value = 0.0159

d) Since p value < 0.05, reject Ho.

Option A is correct.

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

Option A is correct.

Difference Mean Std. Err. DF T-Stat P-value Older Sibling IQ (x) - Younger sibling IQ (y) 2.6 1.0241528 9 2.5386838 0.0159

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