Snow geese feeding trial. 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 LO9 

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 SNOW file. The first and last 5 observations are listed in the table below.

Feeding Trial Diet Weight Change

(%)

Digestion Efficiency

(%)

Acid-

Detergent Fiber (%)

1 Plants -6 0 28.5 2 Plants -5 2.5 27.5 3 Plants -4.5 5 27.5 4 Plants 0 0 32.5 5 Plants 2 0 32 f f f f f 38 Duck Chow 9 59 8.5 39 Duck Chow 12 52.5 8 40 Duck Chow 8.5 75 6 41 Duck Chow 10.5 72.5 6.5 42 Duck Chow 14 69 7 Based on Gadallah, F. L., and Jefferies, R. L. “Forage quality in brood rearing areas of the lesser snow goose and the growth of captive goslings.” Journal of Applied Biology, Vol. 32, No. 2, 1995, pp. 281–282 (adapted from Figures 2 and 3).

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 a = .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 fiber x. Repeat parts a–d for these two variables.

f. Fit the simple linear regression model to the data using x = digestion efficiency.
g. Do you recommend using the model to predict weight change y? Explain.
h. Use the model to form a 95% confidence interval for the mean weight change of all baby snow geese with a digestion efficiency of x = 15%. Interpret the interval.