Chicken diet and weight, Part I. Chicken farming is a multi-billion dollar industry, and any methods that increase the growth rate of young chicks can reduce consumer costs while increasing company profits, possibly by millions of dollars. An experiment was conducted to measure and compare the effectiveness of various feed supplements on the growth rate of chickens. Newly hatched chicks were randomly allocated into six groups, and each group was given a different feed supplement. Below are some summary statistics from this data set along with box plots showing the distribution of weights by feed type.21
Weigh t (in grams)
casein horsebean linseed meatmeal soybean sunflower 100
Mean SD n casein 323.58 64.43 12 horsebean 160.20 38.63 10 linseed 218.75 52.24 12 meatmeal 276.91 64.90 11 soybean 246.43 54.13 14 sunflower 328.92 48.84 12
(a) Describe the distributions of weights of chickens that were fed linseed and horsebean.
(b) Do these data provide strong evidence that the average weights of chickens that were fed linseed and horsebean are different? Use a 5% significance level.
(c) What type of error might we have committed? Explain.
(d) Would your conclusion change if we used α = 0.01?
21Chicken Weights by Feed Type, from the datasets package in R..
Chicken diet and weight, Part II. Casein is a common weight gain supplement for humans. Does it have an effect on chickens? test the hypothesis that the average weight of chickens that were fed casein is different than the average weight of chickens that were fed soybean. If your hypothesis test yields a statistically significant result, discuss whether or not the higher average weight of chickens can be attributed to the casein diet. Assume that conditions for inference are satisfied.