Sibling IQ Scores: There have been numerous studies involving the correlation an

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.

If you are using software, you should be able copy and paste the data directly into your software program. (if you are using online software, please show link to the software) Thanks!

(a) The claim is that the mean difference is positive (d > 0). What type of test is this?
__This is a right-tailed test.
__This is a two-tailed test.
__This is a left-tailed test.

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

Pair ID Older Sibling IQ (x) Younger Sibling IQ (y) difference (d= x-y) 1 83 81 2 2 86 91 -5 3 90 84 6 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 97.3 2.4 s 12.2 10.6 3.8

Explanation / Answer

a)as we are checking if older siblings have higher IQ therfore

This is a right-tailed test.

b)

here std error =std deviation/(n)1/2 =3.8/sqrt(10) =1.20

test statistic =dbar/std error =2.4/1.20 =2.00 (exact value of tdbar =2.01)

c)

p value =0.0383 (excat value of p=0.0377)

please revert for above

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