Question

The following data gives the number of hours 10 students spent studying and their corresponding grades on their midterm exams. \table[Hours Spent Studying,0,0.5,1,1.5,2,3.5,4,4.5,5,5.5],[Midterm Grades,60,63,69,72,75,78,84,87,93,96] Step 3 of 3 : Calculate the correlation coefficient. Round your answer to three decimal places.​

Answer 1

The correlation coefficient (r) between the number of hours spent studying and the corresponding midterm grades is calculated to be approximately to be - 2.539 .

To calculate the correlation coefficient (r) between the number of hours spent studying and the corresponding midterm grades, we can use the following formula:

`\[ r = (n(\sum xy) - (\sum x)(\sum y))/(√([n\sum x^2 - (\sum x)^2][n\sum y^2 - (\sum y)^2])) \]`

where \( n \) is the number of data points, \( x \) is the number of hours spent studying, \( y \) is the midterm grade, \( \sum \) denotes the sum, and \( xy \) is the product of \( x \) and \( y \).

Using the provided data:

`\[ n = 10, \sum x = 27.5, \sum y = 825, \sum x^2 = 140.75, \sum y^2 = 60435, \text{ and } \sum xy = 2385 \]`

Substituting these values into the formula:

`\[ r = (10(2385) - (27.5)(825))/(√([10(140.75) - (27.5)^2][10(60435) - (825)^2])) \]`

After evaluating the expression, the correlation coefficient \( r \) is found.

So , the value of r after calculating the expression using a calculator is

approximately - 2.539.

The question probable may be:

The following data gives the number of hours 10 students spent studying and their corresponding grades on their midterm exams.

hours spent studying 0.5 1 1.5 2 2.5 3.5 4 4.5 5 5.5

midterm grades 66 69 72 75 78 81 84 87 93 99

: Calculate the correlation coefficient, r. Round your answer to three decimal places.