SOLUTION: Agra-Tech Industries has recently introduced feed supplements for both cattle and hogs (pigs) that will increase the rate at which the animals gain weight. Three years of feedlot

Question 1178848: Agra-Tech Industries has recently introduced feed supplements for both cattle and hogs
(pigs) that will increase the rate at which the animals gain weight. Three years of feedlot
tests indicate that steers fed the supplement will weigh an average of 125 pounds more
than those not fed the supplement. However, not every steer on the supplement has the
same weight gain; results vary. The standard deviation in weight-gain advantage for the
steers in the three-year study has been 10 pounds.
Similar tests with hogs indicate those fed the supplement average 40 additional pounds
compared with hogs not given the supplement. The standard deviation for the hogs was
also 10 pounds. Even though the standard deviation is the same for both cattle and hogs,
the mean weight gains differ.
i) Identify two main variables discussed in this scenario.
ii) Compute the coefficient of variation for each variable.
iii) Based on the answers to part ii, which population has data values that are more variable relative to the size of the population mean?
Answer by CPhill(1987) (Show Source): You can put this solution on YOUR website!
Let's break down this problem:
**i) Identify Two Main Variables:**
The two main variables discussed in this scenario are:
1. **Weight Gain Advantage for Steers (Cattle)**
2. **Weight Gain Advantage for Hogs (Pigs)**
**ii) Compute the Coefficient of Variation for Each Variable:**
The coefficient of variation (CV) is a measure of relative variability. It is calculated as:
CV = (Standard Deviation / Mean) * 100%
* **Steers (Cattle):**
* Mean (μ_steers) = 125 pounds
* Standard Deviation (σ_steers) = 10 pounds
* CV_steers = (10 / 125) * 100% = 0.08 * 100% = 8%
* **Hogs (Pigs):**
* Mean (μ_hogs) = 40 pounds
* Standard Deviation (σ_hogs) = 10 pounds
* CV_hogs = (10 / 40) * 100% = 0.25 * 100% = 25%
**iii) Based on the Answers to Part ii, Which Population Has Data Values That Are More Variable Relative to the Size of the Population Mean?**
* **Hogs (Pigs) have a higher coefficient of variation (25%)** compared to Steers (8%).
This means that the weight gain advantage for hogs is **more variable relative to its mean** than the weight gain advantage for steers. Even though both have the same standard deviation, the mean weight gain for hogs is much smaller, making the relative variability larger.

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