In the production of commercial eggs in Europe, four EGGS different types of housing systems for the chickens are used: cage, barn, free range, and organic. The characteristics of eggs produced from the four housing systems were investigated in Food Chemistry (Vol. 106, 2008). 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 organic. A number of quantitative characteristics were measured for each egg, including shell thickness (millimeters), whipping capacity (percent overrun), and penetration strength (newtons). The data (simulated from summary statistics provided in the journal article) are saved in the accompanying file. For each characteristic, the researchers compared the means of the four housing systems. Minitab descriptive statistics and ANOVA printouts for each characteristic are shown (next column). Fully interpret the results. Identify the characteristics for which the housing systems differ.

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Minitab output for Exercise 9.33 Descriptive Statistics: THICKNESS, OVERRUN, STRENGTH Variable HoUSING Mean StDev Minimum Haximum 6 0.s0000 0.01414 0 48000 0.52000 CAGE 10 О.4230 О.0350 0.3700 0.4700 0.5017 0.0279 0.4700 .5500 ORGANIC 6 О.4617 0.0387 0.4300 0.5200 THICKNESS BARN FREE OVERRO BARN 6 513.33 35 501.00 526.00 CAGE 10 О.60 12.91 462.00 502.00 817 510.00 531.00 ORGANIC6 29.17 10.6 .00 544.00 FREE 6 517.80 STREIGTH BAR 6 39.333 .220 37.600 40.300 CAGE 37.320 2.127 33.000 40.200 37932.50 40.60 ORGANIC 6 35.97 3.04 32.60 0. 20 FREE 6 37.27 One-way ANOVA: THICKNESS versus HOUSING Source DE HOUSIN 3 0.034291 0.011430 12.74 o.ooo E:ror 24 Ο.023377 0.000974 Total27 0:057668 MS One-way ANOVA: OVERRUN versus HOUSING Source DE S MS HOUSING 3 10788 3596 33.36 0.000 Exzor 24 2752 115 Total 27 13540 One-way ANOVA: STRENGTH versus HOUSING Source DE HOUSING 3 35.12 11.7 1-70 0.193 Exror 24 16.82 6.87 Total 27 199.94