Answer to Question #280354 in Statistics and Probability for pogi

Question

A herd of 1,500 steer was fed a special high‐protein grain for a month. A random sample of 29 were weighed and had gained an average of 6.7 pounds. If the standard deviation of weight gain for the entire herd is 7.1, test the hypothesis that the average weight gain per steer for the month was more than 5 pounds.

 

Answer 1

Solution:

null hypothesis: H ₀: μ = 5

alternative hypothesis: H _a: μ > 5

$z=\dfrac{6.7-5}{7.1/\sqrt{29}}=\dfrac{1.7}{1.318}=1.289$

From z-score table:

Tabled value for z ≤ 1.28 is 0.8997

1 – 0.8997 = 0.1003

So, the conditional probability that a sample from the herd gains at least 6.7 pounds per steer is p = 0.1003. Should the null hypothesis of a weight gain of less than 5 pounds for the population be rejected? That depends on how conservative you want to be. If you had decided beforehand on a significance level of p < 0.05, the null hypothesis could not be rejected.