2. The owner of Youtbia Farm wants to estimate the mean number of eggs laid per chicken. A sample of 20 chickens shows they laid an average of 20 eggs per month with a standard deviation of 2 eggs per month. Would it be reasonable to conclude that the population mean is 21 eggs?

We reject H₀, we don't have enough evidence for claim mean is reasonable 21 eggs

Step-by-step explanation:

We assume normal distribution, and as n (sample) is 20 minor than 30 we should use t-student tables, then:

1: - Hypothesis test:

Null Hypothesis H₀ μ₀ = 21

Alternative Hypothesis Hₐ μ₀ < 21

We choose one tail test to the left because thye information we have is of 20 eggs by month therefore we have not indication of major production

2. - n = 20 Then degree of fredom is df = n - 1 df = 20 - 1 df = 19

And we will choose 95% of confidence interval so α = 0,05

with these values we go to t-student table to get t (c)

t (c) = 1,729 and t (c) = - 1,729 by symmetry

3. - We need to calculate t (s) as:

t (s) = μ - μ₀) / 2/√n ⇒ t (s) = (20 - 21) * √20 / 2

t (s) = - 1*4,47 / 2

t (s) = - 2,23

4. - Comparison of t (c) and t (s)

t (s) < t (c) - 2,23 < - 1,729

5.-We found that t (s) is in the rejection region we, reject H₀

We don't have enough evidence to claim the mean could reasonable be in 21 eggs