Question

researchers wondered whether the size of a persons brain was related to the individuals 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. click the icon to view the critical values table. a. yes, mri count and iq are linearly related since the linear correlation coefficient is 0.776. b. no, mri count and iq are not linearly related since the linear correlation coefficient is (c) draw a scatter diagram, but use a different plotting symbol for each gender. choose the correct diagram below.

Explanation:

1. Part (a) - (b) (assuming we need to verify the linear - correlation coefficient calculation or make a decision based on it):

• The linear correlation coefficient \(r\) is used to measure the strength and direction of a linear relationship between two variables. A value of \(r = 0.776\) indicates a relatively strong positive linear relationship.
• Since the question seems to be about determining the linear relationship between MRI count and IQ, and the given \(r=0.776\) (a value close to 1 in magnitude for a positive relationship), the answer to the part about linear - relationship (assuming it's asking if there is a linear relationship) is that there is a linear relationship.

1. Part (c) - Drawing a scatter - diagram:

• To draw a scatter - diagram with different plotting symbols for each gender, we need to plot the points where the x - axis represents the MRI count and the y - axis represents the IQ score. For females and males, we use different symbols (e.g., circles for females and squares for males).
• Without seeing the actual options in detail, we need to look for a graph where there are two distinct sets of points (one for females and one for males) with the x - values corresponding to MRI counts and y - values corresponding to IQ scores.

Step1: Analyze linear - correlation coefficient

The value \(r = 0.776\) is relatively close to 1, indicating a positive linear relationship.

Step2: Understand scatter - diagram requirements

We need to plot MRI count on x - axis and IQ on y - axis with different symbols for genders.

Answer:

For the part about linear relationship (assuming it's asking if MRI count and IQ are linearly related): Yes, MRI count and IQ are linearly related since the linear correlation coefficient is 0.776. For the scatter - diagram part, without seeing the options clearly, we look for a graph with two distinct sets of points (one for females and one for males) with MRI count on the x - axis and IQ on the y - axis.