Question

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?

Answer 1

We reject H₀, we don´t have enough evidence for claim mean is reasonable 21 eggs

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