Spring Is Right Around the Corner and That Can Mean

question 42

Multiple Choice

Spring is right around the corner and that can mean only one thing: it's time to incubate some eggs for a fresh crop of chickens to supplement the existing flock for the year. There are three breeds that are popular: Leghorns, Buff Orpingtons, and Cochins, and each has its own strengths and weaknesses. The Leghorns, for example, are superb layers but easily excitable. The Cochins, on the other hand, are very even-tempered but not the best layers. They do have marvelous plumage, with feathers that extend down to their feet. The Buff Orpingtons are good layers, have interesting plumage, and are mid-range in their temperament.
The chicken farmer would like this crop of chickens to produce as many eggs as possible while keeping the noise to a dull roar and having a nice array of birds free-ranging on his lawn during those lazy summer days. He has put the relevant data in table form. Plumage numbers are on a scale from 1-10, with 10 being the most desirable. The egg output is not on a scale, but is instead the average output for the breed, based on years of collecting eggs.
$$\begin{array} { | l | c | c | c | } \hline \text { Bird } & \text { Leghorn } & \text { Cochin } & \text { Buff Orpington } \\\hline \text { Eggs/week } & 5 & 2 & 4.5 \\\hline \text { Plumage } & 3 & 9 & 6 \\\hline \text { Temperment } & 2 & 8 & 5 \\\hline \text { Fertilizer } & 3 & 2 & 4 \\\hline \text { Appetite } & 5 & 4 & 8 \\\hline\end{array}$$ Temperament is actually measured by the average volume of cackling, clucking, and crowing and is measured in decibels per bird. Appetite is measured in ounces of layer pellets per week consumed by each of the breeds, while fertilizer is measured as the output in ounces per week.
-The poultry farmer has in mind the following levels for each of his metrics of interest: a plumage score greater than 75, fertilizer production greater than 80 ounces per week, temperment less than 100 decibels, and an appetite less than 160 ounces of layer pellets per week. When he runs his linear programming model, he discovers that his flock will consist entirely of Leghorn birds. He can picture the sad little faces of his children when he tells them that there will be no variety of birds gracing their front lawn this summer. Help him avoid the embarrassment by selecting a constraint that will ensure that there is some variety in his flock.

• A) 5L + 4C + 8B ? 160
• B) 5L + 4C + 8B ? 160
• C) C + B ? 5
• D) L + C + B ? 5

Understand the relationship between the coefficient of correlation and determination.

Differentiate between various sum of squares in regression analysis (SSR, SSE).

Apply hypothesis testing in the context of regression analysis.

Analyze and interpret correlation in the context of linear relationships.

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Definitions:

Expected Cell Frequency

The predicted number of observations that fall into a specific category or cell within a contingency table.

Sample Size

The number of observations or data points collected in a statistical sample.

Degrees of Freedom

The count of independent pieces of information available to estimate another statistic, crucial in defining the distribution of various test statistics.

Contingency Table

A table used in statistics to display the frequency distribution of variables to show the relationship between them.