Refer to the Food Chemistry (Vol. 106, 2008) study of commercial eggs produced from different housing systems for chickens, Exercise. Recall that the four housing systems investigated were (1) cage, (2) barn, (3) free range, and (4) organic. Twenty-eight commercial grade A eggs were randomly selected from supermarkets-10 of which were produced in cages, 6 in barns, 6 with free range, and 6 organically. A number of quantitative charac teristics were measured for each egg, including penetration strength (Newtons). The data (simulated from summary statistics provided in the journal article) are given in the accompanying table and saved in the EGGS file.

a. Rank the observations in the data set from 1 to 28.
b. Sum the ranks of the data for each housing system.
c. Use the rank sums to find the Kruskal-Wallis test statistic.
d. Based on the result, part c , what do you infer about the strength distributions of the four housing systems?

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Cage: Free: Barn: Organic 34.5 36.8 32.6 38.5 40.2 33.2 36.9 39.2 40.2 33.0 39.0 36.6 37.5 38.1 37.8 34.9 31.5 39.7 37.8 33.5 39.9 40.6 40.0 37.6 39.6 40.3 38.3 40.2