Exercise 4.30 describes a company that advertises that its milled flaxseed conta

Question

Exercise 4.30 describes a company that advertises that its milled flaxseed

contains, on average, at least 3800 mg of ALNA, the primary omega-3 fatty

acid in flaxseed, per tablespoon. In each case below, which of the standard

significance levels, 1% or 5% or 10%, makes the most sense for that

situation?

(a) The company plans to conduct a test just to double-check that its claim is

correct. The company is eager to find evidence that the average amount per

tablespoon is greater than 3800 (their alternative hypothesis), and is not really

worried about making a mistake. The test is internal to the company and there

are unlikely to be any real consequences either way.

(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 at least 3800

mg per tablespoon. If the organization finds evidence that the advertising

claim is false, it will file a lawsuit against the flaxseed company. The

organization wants to be very sure that the evidence is strong, since if the

company is sued incorrectly, there could be very serious consequences.

Explanation / Answer

(a)

Here the test is internal to the company and there are unlikely to be any real consequences either way so we can choose mostly used signficance level 5%.

(b)

Here if reject the null hypothesis " the product contains at least 3800 mg per tablespoon." then consequences are very strong. So we should veru much carefull in rejecting the null hypothesis. That si we should use minimum level of signficance. That is we should use 1% level of signficance.

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