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Refer to the data in the table below. The IQ score and brain volume are listed for each of five different subjects. $$\begin{array}{|l|l|l|l|l|l|}\hline \multicolumn{2}{|l|} {\text { IQ Score and Brain Volume }} \\\hline \text { Subject } & 1 & 2 & 3 & 4 & 5 \\\hline \text { IQ Score } & 87 & 127 & 101 & 94 & 97 \\ \hline \text { Brain Volume }(\mathrm{cm} 3) & 1035 & 1034 & 1173 & 1347 & 1029 \\\hline \hline \end{array}$$ Source of the Data The data in the table were obtained by members of departments at Harvard Medical School, Massachusetts General Hospital, Dartmouth College, Dartmouth Medical School, and the University of California at Davis. Funding for the study was provided by awards from the National Institutes of Health, which is an agency of the U.S. Department of Health and Human Services. Does the source of the data appear to be unbiased?

So as I mentioned before, we're looking at people's excuse I. Q. Scores and brain sizes. Trying to see if there's a correlation between these two. There's a higher I. Q. Score. Mean then you have a bigger brain, you know, 200 I. Q. Big brain moves. Is that true or is that false? We can conduct a statistical analysis to figure that out so to find out if there's a correlation.

Hello In the question, it is given that the I Q is defined to be that issue of mental age, as determined by certain tests to chronological age multiplied by 100. It is given by the equation. Um, Comma C will be cause to embassy in 200 so we have to find the value of Q below of I Q or Q 12. Common 10 and cube at 10. Common. 12. So now we will put the value. The value of them is 12 and sees 10 in 200 so this will be close to 1 20. Okay, the value of em here and the value of C will be well into 100. So 1000 upon 12 will request to 83.33 83 point 33 Okay, we can decide. It is approximately comes to your p three. These are the answer. I hope you understood. Thank you.

So the final question about this is can we conclude that bigger brain higher I. Q. Um While the data does show this that there are greater ice Q scores with larger brains, it just happens that there can be a confounding variable. We don't really know for certain that it is exactly a. Q. Score and brain size that do this. Uh We could look at a larger sample size to see uh if that same correlation appears or if it's just a statistical fluke. So the answer is gonna be no, but you can't just conclude that bigger brain, bigger IQ.

This problem, we are told that the intelligence quotient or eQ is defined to be the ratio of mental age M. A. Is determined by certain tests to chronological age. See a multiplied by 100 stated as an equation Q of M C equals M oversee times 100 Were then asked to find Q of 12, 10 and Q of 10, 12. So q of 12, 10, it's just going to be what happens when we have M equals 12 and C equals 10. So we'd have 12/10 times 100. Which is going to come out to 120 Than Q of 10. 12 Is going to be 10/12 times 100 Which is going to come out to 250 over three Or as a decimal. That would be 83.3 repeating. Yeah.


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