A farmer wants to increase the weight of her lambs and is considering supplement

Question

A farmer wants to increase the weight of her lambs and is considering supplementing their diets with niacin, which is advertised as an effective weight gain supplement. To add niacin to their diets, the farmer would need to purchase a supply, which is fairly expensive. But if it does actually increase the weights of her lambs, it will lead to higher sales for her farm over time. So she conducts an experiment where she compares the weight gains of a sample of lambs on regular feed to a sample that receives an additional niacin supplement.

a. Write an appropriate null and alternative hypothesis for her experiment.

b. In the famer’s perspective, explain the consequence of a Type-I error.

c. In the famer’s perspective, explain the consequence of a Type-II error.

d. Suppose the farmer analyzed her experimental data and got a p-value of 0.03. What would be the appropriate conclusion?

The basal diameter of a sea anemone is an indicator of its age, and in a certain population of anemones, the distribution of basal diameters is approximately normal with a mean of 5.3 cm and a standard deviation of 1.8 cm. Suppose you randomly select five anemones from this population.

a. What is the probability that all five anemones have a basal diameter more than 5.5 cm?

b. What is the probability that the mean basal diameter of the five anemones is more than 5.5 cm?

c. Comparing the probabilities you calculated in parts (a) and (b), which is larger? Even if we changed the values the mean and standard deviation of this population, briefly explain why this must will always be the case.

Explanation / Answer

a. The null hypothesis is the hypothesis of no difference, that means there is no difference in weight gain for lambs on regular feed and additional niacin supplement. Thus, H0:mun-mur=0. The alternative hypothesis is the tentative proposition which the researcher wants to prove, that there will be increase in weight for lambs on additional niacin supplement compared to lambs on regular feed. Thus, H1:mun-mur>0

b. The Type I error occurs when the researcher incorrectly reject true null hypothesis. Therefore, If there is no difference in weight for lambs on regular supplement and niacin supplement, but the researcher concludes that there is increase in weight for lambs on niacin supplement, she commits Type I error and end up purchasing expensive supply.

c. The Type II error occurs when researcher fails to reject a false null hypothesis. That is, when there is increase in weight for lambs on niacin supplement but researcher concludes that there is no difference in weight for lambs on regular feed and niacin supplement, researcher commits Type II error, and incur loss in terms of sales.

d. Per rejection rule based on p value, reject null hypothesis if p value is less than alpah=0.05. Here, 0.03<0.05, therefore, reject H0 and conclude that there is significant increase in weight for lambs on niacin supplement compared to those on regular feed.

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