Question

4.30 Flaxseed and Omega-3 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 mg of ALNA, the primary omega-3.

1. 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 mg. What are the null and alternative hypotheses?
2. 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 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 mg. What are the null and alternative hypotheses?

Answer 1

$\mu$ : Average ALNA, the primary omega-3 per one table spoon of the product

Case 1:

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 mg.

The Company To test : Average is higher than 3800mg therefore;

Null hypothesis : H_o : $\mu$ = 3800

Alternate hypothesis : H_a : $\mu$ > 3800

Case 2: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 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 mg

Consumer organization to test : actual average amount of omega-3 is less than 3800 mg

Null hypothesis : H_o : $\mu$ = 3800

Alternate hypothesis : H_a : $\mu$ < 3800

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The null and alternative hypotheses are two mutually exclusive statements about a population. A hypothesis test uses sample data to determine whether to reject the null hypothesis.

Null hypothesis (H₀)

The null hypothesis states that a population parameter (such as the mean, the standard deviation, and so on) is equal to a hypothesized value. The null hypothesis is often an initial claim that is based on previous analyses or specialized knowledge.

Alternative Hypothesis (H₁)

The alternative hypothesis states that a population parameter is smaller, greater, or different than the hypothesized value in the null hypothesis. The alternative hypothesis is what you might believe to be true or hope to prove true.

One-sided and two-sided hypotheses

The alternative hypothesis can be either one-sided or two sided.

Two-sided

Use a two-sided alternative hypothesis (also known as a nondirectional hypothesis) to determine whether the population parameter is either greater than or less than the hypothesized value. A two-sided test can detect when the population parameter differs in either direction, but has less power than a one-sided test.

One-sided

Use a one-sided alternative hypothesis (also known as a directional hypothesis) to determine whether the population parameter differs from the hypothesized value in a specific direction. You can specify the direction to be either greater than or less than the hypothesized value. A one-sided test has greater power than a two-sided test, but it cannot detect whether the population parameter differs in the opposite direction.