Question: Variances & Covariances

Given the following data below:

Subject (i) 1 2 3 4 5 6 7 8 9 10 11
BW 515 286 469 410 461 436 479 198 389 262 536
LFC 32.5 26.8 11.41 14.85 23.64 23.82 29.84 21.83 24.65 22.5 26.0

BW (brain weight in grams) LFC (large fiber count >7.5 microns in diameter in thousands)

A. Calculate the means, the variances, and the covariance. What are the units of each?

B. Earlier published work on a larger sample (n =34) found a significant though moderate correlation (r = +0.40) between these variables. Is the strength of the relationship in the present study different (stronger or weaker) from the earlier study? Formally test the hypothesis. [You may either treat the value +0.40 as a parameter or treat both the 1963 and the 1969 correlations as sample statistics – either way is fine]