Question

Studies have shown that omega-3 fatty acids have a wide variety of health benefits. Omega- 3 oils can be found in foods such as fish, walnuts, and flaxseed. A company selling milled flaxseed advertises that one tablespoon of the product contains, on average, at least \(3800 \mathrm{mg}\) of ALNA, the primary omega-3. (a) The company plans to conduct a test to ensure that there is sufficient evidence that its claim is correct. To be safe, the company wants to make sure that evidence shows the average is higher than \(3800 \mathrm{mg} .\) What are the null and alternative hypotheses? (b) Suppose, instead, that a consumer organization plans to conduct a test to see if there is evidence against the claim that the product contains an average of \(3800 \mathrm{mg}\) per tablespoon. The consumer organization will only take action if it finds evidence that the claim made by the company is false and that the actual average amount of omega- 3 is less than \(3800 \mathrm{mg}\). What are the null and alternative hypotheses?

Short answer

For the company, null hypothesis, H0: µ = 3800mg and alternative hypothesis, H1: µ > 3800mg. For the consumer organization, null hypothesis, H0: µ = 3800mg and alternative hypothesis, H1: µ < 3800mg.

Step-by-step solution

Establishing Null and Alternative Hypothesis from Company's Perspective

From the perspective of the company, the null hypothesis (H0) would be that the average quantity of omega-3 fatty acids in a tablespoon of milled flaxseed is equal to 3800 mg. The alternative hypothesis (H1) would be that the average quantity of omega-3 fatty acids in a tablespoon of milled flaxseed is greater than 3800 mg. So, H0: µ = 3800mg and H1: µ > 3800mg. Here, µ refers to the average quantity of omega-3 acid.

Establishing Null and Alternative Hypothesis from Consumer Organization's Perspective

If a consumer organization is considering this case, the null hypothesis (H0) would still be that the average quantity of omega-3 fatty acids in a tablespoon of milled flaxseed equals 3800mg – this is because null hypotheses always involve a statement of equality. However, the alternative hypothesis (H1) would be that the average quantity of omega-3 fatty acids in a tablespoon of milled flaxseed is less than 3800mg. As such, from the consumer organization's perspective, null hypothesis, H0: µ = 3800mg and alternative hypothesis H1: µ < 3800mg.