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

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.