Weaning weights are used to evaluate di erences in growth potential of calves. A random sample of 41 steer calves is taken from a large ranch. The sample yields a mean weaning weight of 578 with a standard deviation of 87 lbs. This particular ranch is targeting an average weaning weight of 610 lbs. Perform a hypothesis test using = 0:01 to determine if the average weaning weight of cows at this ranch is di erent than 610 lbs.

We accept H₀ the weaning weights of cows at this ranch is 610 lbs

Step-by-step explanation:

We assume normal distribution

Population mean μ₀ = 610 lbs

Population standard deviation unknown

sample size n = 41

degree of fredom df = n - 1 df = 41 - 1 df = 40

Sample mean X = 578 lbs

Sample standard deviation s = 87

As we don't know standard deviation of the population we will use t - student test, furthemore, as we are looking for any difference upper and lower we are in presence of a two tails test

Test Hypothesis Null hypothesis H₀ X = μ₀

Alternative hypothesis Hₐ X ≠ μ₀

Now at α = 0,01, df = 40 and two tail test we find t = 2,4347

We have in t table

30 df t = 2,457 for α = 0,01

60 df t = 2,390 for α = 0,01

Δ = 30 0,067

10 x? x = 0,022

then 2,457 - 0,022 = 2,4347

t = 2,4347

Now we compute the interval:

X ± t * (s/√n) ⇒ 578 ± 2,4347 * (87/√41)

578 ± 2,4347 * 13,59

578 ± 33,09

P [ 578 + 33,09; 578 - 33,09 ]

P (611,09; 544,91]

We can see that vale 610 = μ₀ is inside the iinterval, so we accept H₀ the weaning weight of cows in the ranch is 610 lbs