Question

1. The following matrix displays the bivariate correlations between family size (X), weekly grocery bill (Y), and income (Z) for a random sample of 50 families.

             X          Y          Z   

X         1.00      .60       .20

Y          .60      1.00      .30

Z          .20       .30      1.00

1. First, list the values of the 3 unique correlations, identifying the two variables in each correlation in some way. (r_xy = ?; r_xz = ? r_yz = ?)
2. Which of the correlations is statistically significant at the .05 level? Be sure to record the information on which you base these conclusions. (This implies you will need to perform a hypothesis test assessing whether each correlation is large enough to suggest that a real association exists in the population from which the sample was drawn.)

Answer 1

a. The three unique correlation coefficient is r_xy = 0.6; r_xz = 0.2, r_yz = 0.3

n=50

b) We have to test the following hypothesis

So, we will use the t test, we have

which follows n-2 df.

For each we will calculate,

The p-value is < .00001 <0.05 for t₁. We reject the null hypothesis and there is real association exists in the population from which the sample was drawn.

The p-value is .163815. > 0.05 for t2 We accept the null hypothesis and there is no real association exists in the population from which the sample was drawn.

The p-value is .034288. The result is significant at p < .05. for t_3. We reject the null hypothesis and there is real association exists in the population from which the sample was drawn.