The creators of a program that promises to improve typing speed collect data on the time spent on the program (in hrs) and typing speed (in wpm) of a random sample of 25 users to see if there is linear correlation between the two variables. Use the Data Analysis Toolpak to answer the questions below.

$\left(B\right)$ Find $r$.

• A. 0.857
• B. -0.857
• C. 0.735
• D. -0.735

Answer: (A)

Verified step by step guidance

1. Step 1: Organize the data into two lists or columns: one for the time spent on the program (in hours) and one for the typing speed (in words per minute). Here, the time data is [2, 20, 15, 6, 4, 1.5, 7, 21, 3, 4, 13, 12, 2, 5, 17, 14, 13, 15, 7, 6, 11, 9, 6, 7, 8] and the speed data is [39, 71, 65, 53, 42, 36, 55, 84, 41, 44, 64, 66, 42, 61, 72, 63, 62, 60, 59, 67, 64, 60, 57, 61, 62].
2. Step 2: Calculate the mean (average) of the time data and the mean of the speed data. The mean is found by summing all values in each list and dividing by the number of observations (25 in this case).
3. Step 3: Calculate the covariance between time and speed. Covariance measures how two variables vary together and is calculated by summing the product of the deviations of each pair of observations from their respective means, then dividing by the number of observations minus one.
4. Step 4: Calculate the standard deviation of the time data and the standard deviation of the speed data. The standard deviation measures the spread or dispersion of the data points around the mean.
5. Step 5: Calculate the Pearson correlation coefficient \(r\) using the formula: \[r = \frac{\text{covariance}(X, Y)}{\text{standard deviation of } X \times \text{standard deviation of } Y}\] where \(X\) is time and \(Y\) is speed. This value will indicate the strength and direction of the linear relationship between time spent on the program and typing speed.