Question

The following is a correlation matrix among 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

Which of the correlations are significant at the .05 level?

Answer 1

The correlation coefficients between family size (X) and weekly grocery bill (Y), and between weekly grocery bill (Y) and income (Z) are significant at the 0.05 level.

Step-by-step explanation:

Correlation Coefficients:

The correlation matrix provided shows the correlations among family size (X), weekly grocery bill (Y), and income (Z) for a random sample of 50 families. The matrix is as follows:

• X and Y have a correlation coefficient of 0.60
• X and Z have a correlation coefficient of 0.20
• Y and Z have a correlation coefficient of 0.30

Significance at the 0.05 Level:

To determine which correlations are significant at the 0.05 level, we compare the correlation coefficients to the critical values. Since the sample size is 50, the degree of freedom (df) is 48.

• X and Y: The critical value for a two-tailed test at the 0.05 level with df = 48 is approximately ±0.27. Since |0.60| > 0.27, the correlation between X and Y is significant.
• X and Z: The critical value for a two-tailed test at the 0.05 level with df = 48 is approximately ±0.27. Since |0.20| < 0.27, the correlation between X and Z is not significant.
• Y and Z: The critical value for a two-tailed test at the 0.05 level with df = 48 is approximately ±0.27. Since |0.30| > 0.27, the correlation between Y and Z is significant.

In summary, the correlations that are significant at the 0.05 level are between X and Y, and between Y and Z.