Question

a high school softball coach recorded the average amount of time spent at batting practice each week and the total nur season for each player. the results are shown in the table below.
batting practice (minutes) 60 90 100 105 110 110 115 120 125 140
number of hits 20 13 11 22 30 20 31 35 31 28
determine the approximate value, description, and interpretation of the correlation coefficient for the given data.
correlation coefficient description of linear correlation interpretation of correlation coefficient
0.59 positive correlation as a player gets more hits through the season, she increases the amount of time spent in batting practice.
-0.65 negative correlation the more time a player spends in weekly batting practice, the greater number of hits she can expect to get in the season.
0.65 no correlation weekly batting practice time and the number of hits in a season are not related.

Explanation:

Step1: Analyze the relationship between variables

We are looking at the relationship between batting practice time (independent variable) and number of hits (dependent variable). A positive correlation coefficient means that as one variable (batting practice time) increases, the other variable (number of hits) also tends to increase.

Step2: Evaluate the values

The correlation coefficient value of \(0.59\) is positive. A value of \(0.59\) indicates a moderate positive linear correlation. The interpretation should be based on the direction of the relationship (positive - as practice time increases, hits increase). The value \(- 0.65\) is negative (opposite relationship which is not the case here as more practice should relate to more hits in a positive way), and \(0\) correlation (no relationship) is incorrect as there is a visible trend.

Answer:

Correlation Coefficient: \(0.59\), Description of Linear Correlation: Positive correlation, Interpretation of Correlation Coefficient: The more time a player spends in weekly batting practice, the greater number of hits she can expect to get in the season.