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Chapter 8: Q1 (page 371)

Vitamin C and Aspirin A bottle contains a label stating that it contains Spring Valley pills with 500 mg of vitamin C, and another bottle contains a label stating that it contains Bayer pills with 325 mg of aspirin. When testing claims about the mean contents of the pills, which would have more serious implications: rejection of the Spring Valley vitamin C claim or rejection of the Bayer aspirin claim? Is it wise to use the same significance level for hypothesis tests about the mean amount of vitamin C and the mean amount of aspirin?

Short Answer

Expert verified

Rejection of the Bayer pills aspirin claim will have serious implications compared to the rejection of the Spring Valley tablets vitamin C claim.

No, it would not be wise to use the same level of significance for testing both claims.

Step by step solution

01

Given information

It is given that a bottle of Spring Valley tablets has a label stating an amount of 500 mg of vitamin C.

Another bottle of Bayer pills has a label stating an amount of 325 mg of aspirin.

02

Consequence of rejection of claim

A claim is made about the mean amount of vitamin C in a given bottle of Spring Valley tablets.

Another claim is made about the mean amount of aspirin in a bottle of Bayer pills.

Since aspirin is a type of drug and improper dosage of a drug can have severe implications on the consumers' health, the rejection of the claim regarding the mean amount of aspirin is more severe than the rejection of the claim regarding the mean amount of vitamin C.

03

Suitable level of significance

The level of significance in hypothesis testing is the acceptable value of the Type I error which is the error made by rejecting the claim when it is actually true.

Thus, a smaller level of significance would reduce the possible amount of acceptable Type I error that can be committed.

Since the rejection of the claim regarding the mean amount of aspirin can have grave consequences, the possible amount of error should be as small as possible.

Therefore, a smaller level of significance would be wise to use in the case of the claim pertaining to the mean amount of aspirin compared to the level of significance used to test the claim on the mean amount of vitamin C.

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