Botanists at the University of Toronto conducted a series of experiments to investigate the feeding habits of baby snow geese (Journal of Applied Ecology, Vol. 32, 1995). Goslings were deprived of food until their guts were empty and then were allowed to feed for 6 hours on a diet of plants or Purina ® Duck Chow ®. For each feeding trial, the change in the weight of the gosling after 2.5 hours was recorded as a percentage of the bird's initial weight. Two other variables recorded were digestion efficiency (measured as a percentage) and amount of acid-detergent fiber in the digestive tract (also measured as a percentage). Data on 42 feeding trials are saved in the SNOWGEESE file. The first and last 5 observations are listed in the table below.

a. The botanists were interested in the correlation between weight change (y) and digestion efficiency (x). Plot the data for these two variables in a scatterplot. Do you observe a trend?
b. Find the coefficient of correlation relating weight change y to digestion efficiency x. Interpret this value.
c. Conduct a test to determine whether weight change y is correlated with digestion efficiency x. Use α = .01.
d. Repeat parts b and c, but exclude the data for trials that used duck chow. What do you conclude?
e. The botanists were also interested in the correlation between digestion efficiency y and acid-detergent fibe x. Repeat parts a - d for these two variables.

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Weight Digestion Change Eficiency Detergent Acid Feeding Trial Diet Fiber (%) 28.5 27.5 27.5 32.5 32 1 Plants 2 Plants 2.5 Plants 4 Plants 5 Plants 38 Duck Chow 39 Duck Chow 12 40 Duck Chow 41 Duck Chow 42 Duck Chow 59 52.5 75 72.5 69 8.5 8.5 10.5 14 6.5