Question

A researcher want to know if there is a relationship between sleep and anxiety. The researcher randomly selected n = 5 participants and asked each to rate their sleep quality and anxiety level on a scale of 1 to 5. The data are below:

Sleep
X
Anxiety
Y
2
2
3
3
2
2
4
2
5
2
Calculate Pearson's r
Options:
A) 0.8
B) -0.2
C) 0.5
D) -0.6

Answer 1

To calculate Pearson's r, substitute the values into the formula and perform the calculation. Therefore, the answer is A) 0.8.

Step-by-step explanation:

To calculate Pearson's r, we need to find the covariance and the standard deviations of the two variables. The formula for Pearson's r is:

r = (Σ(X - mean(X))(Y - mean(Y))) / √(Σ(X - mean(X))^2Σ(Y - mean(Y))^2)

Using the given data: X = [2, 2, 3, 3, 2] and Y = [2, 4, 4, 2, 5], we can substitute the values into the formula and calculate r. After performing the calculations, we get r = 0.8.

Therefore, the answer is A) 0.8.

Answer 2

In this case, the value of Pearson's r is approximately -0.6.

The correct answer is B) -0.6.

Step-by-step explanation:

To calculate Pearson's r, we need to find the correlation coefficient between the sleep and anxiety ratings. From the given data, we can calculate the mean and standard deviation for both variables.

The formula for Pearson's r is:

r = (Σ((X - X`)(Y - Y`)) / (n * sX * sY)

where X is the sleep rating, Y is the anxiety rating, X` is the mean of X, Y` is the mean of Y, sX is the standard deviation of X, sY is the standard deviation of Y, and n is the number of participants.

By substituting the values into the formula, we get:

r = ((2-3)(2-2.6) + (2-3)(4-2.6) + (3-3)(2-2.6) + (3-3)(5-2.6) + (4-3)(2-2.6)) / (5 * 0.632 * 1.673)

Calculating this expression gives r ≈ -0.6 (rounded down)

Therefore, the correct answer is B) -0.6.

Your question is incomplete, but most probably the full question was:

A researcher want to know if there is a relationship between sleep and anxiety. The researcher randomly selected n = 5 participants and asked each to rate their sleep quality and anxiety level on a scale of 1 to 5.

The data are below:

Sleep (X) Anxiety (Y)

2 2

2 4

3 2

3 5

2 2

Required:

Calculate the value of Pearson's r.

Options:

A) 0.8

B) -0.2

C) 0.5

D) -0.6