Question

the heights (in inches) of 8 high school students and their scores on an iq test are shown in the attached data table with a sample correlation coefficient r of 0.225. remove the data entry for the student who is 59 inches tall and scored 96 on the iq test from the data. describe how this affects the correlation coefficient r. click the icon to view the data set. the new correlation coefficient r gets stronger, going from 0.225 to . (round to three decimal places as needed.)

Explanation:

Step1: Calculate new correlation coefficient

Without the actual data - set values, we assume we would use the formula for the sample correlation coefficient $r=\frac{\sum_{i = 1}^{n}(x_i-\bar{x})(y_i - \bar{y})}{\sqrt{\sum_{i=1}^{n}(x_i-\bar{x})^2\sum_{i = 1}^{n}(y_i-\bar{y})^2}}$. After removing the out - lying data point (the student with height 59 inches and IQ score 96), we recalculate this formula with $n=7$ instead of $n = 8$. In general, if an outlier is removed and it was weakening the correlation, the new correlation coefficient will increase.

Step2: Assume a trend

Since we know the correlation gets stronger and was originally 0.225, we can assume that the new correlation coefficient will be larger. Let's assume we have calculated the new correlation coefficient using statistical software or a calculator with the remaining 7 data points.

Answer:

0.350 (This is a made - up value for illustration purposes as the actual data set is not provided. In a real - world scenario, you would calculate the new $r$ value using the formula with the remaining data points.)