The Golden Comet Is a Hybrid Chicken That Is Prized $5.0$

question 15

Essay

The Golden Comet is a hybrid chicken that is prized for its high egg production rate and gentle disposition. According to recent studies, the mean rate of egg production for 1-year-old Golden Comets is $5.0$ eggs/week.

Sarah has 39 1-year-old hens that are fed exclusively on natural scratch feed: insects, seeds, and plants that the hens obtain as they range freely around the farm. Her hens exhibit a mean egg-laying rate of $5.2$ eggs/day.
Sarah wants to determine whether the mean laying rate $\mu$ for her hens is higher tha the mean rate for all Golden Comets. Assume the population standard deviation to be $\sigma = 1.1 \mathrm { eggs } /$ day.
i. State the appropriate null and alternate hypotheses.
ii. Compute the value of the test statistic.
iii. State a conclusion. Use the $\alpha = 0.01$ level of significance.

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Definitions:

Constant Returns

A situation in economics where increasing the scale of production does not affect the long-run average cost of production, implying it remains constant.

Initial Plant Sizes

The original capacity or scale of a facility when it first begins operations.

Purely Competitive

Characterizes a theoretical market structure emphasizing perfect competition, where numerous small firms face no barriers to entering or exiting the market.

Long Run

A period in which all inputs, including capital, are variable, allowing firms to adjust all factors of production.