Question

3. A local college is studying the number of credit hours students take and how many total minutes they spend reading for fun/pleasure (e.g., non-class-related materials). They don’t know whether to expect that studentswill read more or less when enrolled in a lot of classes/hours or fewer hours. They study 68 students and find a correlation of -0.30.

(A) State the decision rule for the 0.05 significance level. (6) Reject H0 if t > _________

(B) Compute the value of the test-statistic: __________________ (12)

(C) Can we conclude that the correlation in the population is different than zero? (6) Select one:

“Reject H0” or “do not reject H0”
We conclude that the correlation in the population is

zero.

(can or cannot) (less than or greater than)

(D) Explain what this means – how are these variables related. Is it strong, weak, moderate? Estimate a scatterplot of these data with a rough sketch – be sure to label the axes. Think about what to put on the x- axis and what to place on the y-axis. (6)

Answer 1

Answer 3:

For testing of correlation -

To test for significance of the linear correlation, we can perform a hypothesis test,

The null hypothesis being the two variables have 0 correlation against

the alternative hypothesis the two variables are correlated.

This being a two – sided test

Now, if the value of the test statistic is greater than the critical value, we reject the null hypothesis else we fail to reject the null hypothesis

The test statistic for this test would be t = [r x (n - 2) ^0.5]/ (1 – (r^2)) ^0.5, the test statistic t follows the t – distribution with (n - 2) degrees of freedom under the null hypothesis

Reject null if t > 1.9966 (value taken from t – distribution table)

Here, n = 68 and r = -0.30

Substituting all values, we get t = -2.5549

Or |t| = 2.5549

Since, t > 1.9966, Reject H0

We conclude that the correlation in the population is not zero

Answer D:

Since, the value of the correlation coefficient is negative, the variables are negatively related.

The value of the coefficient is -0.30 which indicates a moderate relationship.

A rough sketch is given below -

where X - Axis represents the number of credit hours students take and Y - Axis represents the number of total minutes they spend reading for fun / pleasure