Question

Researchers wondered whether the size of a person's brain was related to the individual's mental capacity. They selected a sample of 5 females and 5 males and measured their MRI image pixel counts and IQ scores. The data is reported to the right Complete parts (a) through (d) below EEB Click the icon to view the critical values table Females MRI Males IQ 833868 131,001,121 140 790,619 135 ,079,550 141 857,782 133 924.059 135 951,545 37 935,494 141 991,305 13 955,003 139 IQ MRI (a) Draw a scatter diagram treating MRI count as the explanatory variable and IQ as the response variable. Choose the correct diagram below. O A. O D. IQ I0 MRI MRI 1,000 1,000 760 780 780,000 1,080,000 780,000 130 145 130 145 MRI I0 (b) Compute the linear correlation coefficient between MRI count and IQ. Are MRI count and IQ linearly related? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. Round to three decimal places as needed) OA. No, MRI count and lQ are not linearly related since the linear correlation coefficient is УВ Yes, MRI count and IQ are linearly related since the linear correlation coefficient is 0.799 (c) Draw a scatter diagram, but use a different plotting symbol for each gender Choose the correct diagram below O A O B. C. OD. MRI IQ MRI 1,080, 1,080 780.0 780 0 145 780,000 1,080,000 MRI 780,000 1,080,000 MRI 130 130 145 IQ (d) Compute the linear correlation coefficient between MRl count and IQ for females. Compute the linear correlation coefficient between MRI count and IQ for males. The linear correlation coelficient for females is 0.773 The linear correlation coetficient for males is 0.584 Round to three decimal places as needed.) Are MRI count and 1Q inearly related? Because the corelation coetmfcient tor temales ispositive and the absolute value of this correlation coeticient, 0 Tr3, s Because the correlation coetficient for males is pastive and the absolute value of this correlation coefficient, 0564, is (Round to three decimal places as needed) than the cntical value for the temale data set, relation exists between MRI Count and IQ for temales Vthan the critical value for the mele data set relation exists between MRI count and IQ for males Are MRI count and IQ linearly related? Because the correlation coemicient tor temales iS positive and the absolute value of this correlation coemcient, 0 773·is Because the cortion coetticient tor males is positve and the absolute value ot this correlation coetticient, D 564. i (Round to three decimal places as needed) thnthe critical valuc for the female data set, ▼ | relation exists between MRI count and IQ for Temals rtical value tor the male data set, ▼ I relation ex sts between MRI count and IQ for males greater not greater Enter your answer in the edit fields and then click Check Answer Arc MRI count and IQ lincarly related? Because the comelation coefficient for females is positive and the absolute value of this correlation coefficient, 0.773, is (Round to three decimal places as needed) Enter your answer in the edit fields and then click Check Answer. I thอn | | the critical value for the female date set relation exists between MRI count and lQ for females Because the coreiation cooficient tor males s positive and the atbsolute value of this.corelation cooficient (0 584 an he citical vaue for the male dala set than the critical valuc for the male data set sts betwoon MRI count and iQ for males a negative a positive para obteher una 3 0.997 4 0.950 5 0.878 6 0.811 7 0.754 8 0.707 9 0.666 10 0.632 11 0.602 12 0.576 13 0.553 14 0.532 15 0.514 16 0.497 17 0.482 18 0.468 19 0.456 20 0.444 21 0.433 22 0.423 23 0.413 24 0.404 25 0.396 26 0.388 27 0.381 28 0.374 29 0.367 30 0.361

Answer 1

because the correlation is positive and the absolute value of correlation coefficient is 0.799
which is greater than 0.707 the critical value

a positive relation exists between MRI and IQ for females