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 counts and IQ scores. The data is reported to the right. Complete parts ​(a) through ​(d) below.
Females Males
MRI IQ MRI IQ
816,932 133 1,001,121 140
833,868 132 1,038,436 139
856,472 140 1,079,550 141
866,662 130 924,059 136
948,066 133 955,033 139

(a) Draw a scatter diagram treating MRI count as the explanatory variable and IQ as the response variable.

(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 answe box to complete your choice.

A. No, MRI count and IQ are not linearly related since the linear correlation coefficient is _____.

B. Yes, MRI count and IQ are linearly related since the linear correlation coefficient is _____.

Answer 1

Answer:

Step-by-step explanation:

Given that 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 counts and IQ scores.

The data is reported to the right. Complete parts ​(a) through ​(d) below.

We want scatter plot for IQ vs MRI in general.

So we group data into two columns X for MRI and Y for IQ and draw scatter plot

MRI IQ

 

816932 133

1001121 140

833868 132

856472 140

866662 130

1038436 139

1079550 141

924059 136

a) Scatter plot is attached as a file

b) correlation coefficient = Cov (x,y)/S_x S_y = 0.729889

B) Yes, MRI count and IQ are linearly related since the linear correlation coefficient is _____.0.729889 >0.5 and near to 1 than to 0

There is a positive moderate correlation between x and y (linear)

Download xlsx