Most of us would like science to find ways to extend our lives. Genetic research has found some promising variants of genes in other organisms that greatly increase life span. Some mutations in the gene daf-2 cause the worm Caenorhabditis elegans to live almost three times as long as normal worms. But does this greater life span come at a cost? Below are data for the average life span (in days) of worms having one of 14 different mutations at the daf-2 gene, along with data on the number of offspring produced during their lives (expressed as a percentage of number of offspring of normal unmutated worms) (Gems et al. 1998). Here we wish to calculate the correlation between these variables.

a. Both variables have positive skew. Find an appropriate transformation to reduce the skew (you will find that skew can be reduced but not altogether eliminated).

b. Include a plot of the transformed data. What trend is suggested?

c. Is life span significantly correlated with number of offspring? Answer using the transformed data.

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daf-2 mutation e1365e1365 m577m577 sa193sa193 e1371e1371 Life span (days) 28.228.2 25.825.8 33.533.5 31.831.8 Relative number of offspring 101101 9595 9696 9999