Instructions: Please answer the following questions as thoughtfully, accurately and completely as you can.

---

1. Using the NRC Feed Table data shown above, calculate the 95% confidence interval for crude protein content of intensively managed pasture and immature legume silage. Interpret your results highlighting the implications for balancing rations of dairy cows. (Hints: Lower limit of 95% confidence interval = Means - 2 SD and the upper limit of 95% confidence interval = Means + 2 SD)

   

	Pasture	Immature Silage
Average CP (% of DM)	26.5	23.2
Standard deviation (SD)	5.6	2.1
2 Standard Deviations	11.2	4.2
Mean – 2 SD (lower limit of 95% confidence interval)	15.3	19
Mean + 2 SD (upper limit of 95% confidence interval)	37.7	27.4

The larger variation in pasture CP reflects the fact that samples were collected and analysis results were averaged over all stages of maturity.  In contrast, by grouping the silage in immature, mid-maturity and mature, the NRC committee has “reduced” variability associated with silage legume as a feed. Thus ration can be formulated with increased confidence when one has multiple categories to help characterize the forage/silage at hand and reduce the expected variability around the mean value. Thus, if one knew the stage of growth of the pasture and group them in three categories like the committee did for the legume silage, one could have more confidence in strategies of protein supplementation of grazing cows.

The higher variability of pasture CP makes protein supplementation of cows in pasture more difficult than if the confidence interval was narrower as in the case of immature alfalfa.

---

2. The graph below shows the means (stars) and the 95% confidence interval (range ←→) for the crude protein (CP) in mid-maturity legume forage. Using your understanding of statistics, indicate whether you should consider the CP in immature alfalfa silage different from the CP level of mature alfalfa silage. Explain

    

Although on average CP in immature alfalfa silage is higher (23.2) than in mature alfalfa silage (20.3), any particular sample of alfalfa categorized as immature may take a value between 19.0 and 27.4 whereas the expected range for mature alfalfa is 16.7 to 23.9. As these two ranges overlap to a great extent, they are not “significantly” different (statistically).  This exercise points to the importance of doing analysis on each “silage sample” and stay away from book value for forage composition when one balance rations for cows in the “real-world.”

---

3. Rank and discuss your reasoning for the expected variation in composition of the following feeds: (a) silages, (b) ethanol industry by-products, (c) home-grown corn grain, (d) minerals supplements.

d =Mineral feed have a very constant composition. These are chemical either commercially synthesized (sodium bicarbonate) or extracted from rock (calcium carbonate).

c = home-grown corn grain: Seed have a fairly constant composition that is altered by genetic and breeding and seasonal condition, but they are harvested when the plant has reached its full maturity.

b = Ethanol by-products may or may not be variable depending how the processing plant handles the by-product (water addition / removal, addition of “nutrient rich” solubles to a solid by-product, etc.)

a = Silages are likely to have the largest variability because the producer decides on cutting time (immature to  mature) and because the quality of the preservation in the silo add an important source of variation.

---

4. Scenario: Imagine you are a dairy consultant and you performed a corn silage analysis on November 15, December 23, and January 12. The crude protein results were 8.0%, 9.2% and 8.8% of the dry matter. It is now January 20 and you need to reformulate the diet for a group of high producing cow.

Question: Should you enter 8.8% for corn silage crude protein in your ration balancing software, should you use 9.0% (the average of late December and early January analyses) or 8.5% (the average of all three available results)? Explain how you would decide what is best.

    The correct answer depends on whether the analyses were from the same silo or from different silos; or from a bunker silo versus an upright silo.  In general, if the silage is from the same silo (which include the harvest of a group of field in a selected date), the average of all previous analysis is a better predictor of what is remaining in the silo. However, if a new silo was opened on January 5^th, and we know that it was harvested on a different date/field that the previous silo, then only the analysis of January 12 should be used in balancing ration with that silage.

---

5. Scenario: You are formulating a 60% forage dairy ration for a high producing group of cows. Because this level of forage inclusion is fairly high for high producing cows, you want to minimize the variation in forage NDF in the ration. You have three silos to choose from. The forages in all three silos have a mean NDF content of 40% of DM with a standard deviation of 2.5% of DM.

Question: What should be your forage feeding strategy? Explain.

     A. Take silage from one of the silos only.
     B. Take half of silage needed from silo 1 and the other half either from silo 2 or silo 3.
     C. Take a third of the silage needed from each of the three silos.
     D. It doesn't matter how many silos we are using because the standard deviation in each silo is the same.

Answer: 3

Weiss paper indicates that increasing the number of ingredients that contribute to a particular nutrient reduces the variation around the target (desired) concentration of that nutrient in the mixture of feeds (i.e., in the diet). The paper gives the example of a diet that has 60% forage and has either one forage (60% of diet is forage A), two forages (30% of the diet is forage A and 30% is forage B), or three forages (20% of the diet is forage A, B, and C). Since all forages have the same average NDF, all diets also have the same average concentration of forage NDF (24%). The SD for the diets with one, two, and three forages is 1.50, 1.08, and 0.89.