Many consumer groups feel that the U. S. Food and Drug Administration (FDA) drug approval process is too easy and, as a result, too many drugs are approved that are later found to be unsafe. On the other hand, a number of industry lobbyists have pushed for a more lenient approval process so that pharmaceutical companies can get new drugs approved more easily and quickly. Consider a null hypothesis that a new, unapproved drug is unsafe and an alternative hypothesis that a new, unapproved drug is safe. a. Explain the risks of committing a Type I or Type II error.
b. Which type of error are the consumer groups trying to avoid? Explain.
c. Which type of error are the industry lobbyists trying to avoid? Explain.
d. How would it be possible to lower the chances of both Type I and Type II errors?

A) The risk of committing Type I error would imply that an unsafe drug is approved. However, the risk of committing a Type II error would imply that a drug is safe but not approved.

B) They are trying to avoid type I error because they don't want drugs that are unsafe to be approved.

C) They are trying to avoid type II errors because the companies would have to continue testing even when the drugs are safe.

D) To lower the chances of type I error, the significance level has to be reduced and they need to make sure that the tests are run for longer periods so that a good representation of the sample size would have been tested which means we are increasing the credibility of the test results.

To lower the chances s of type II error, we have to ensure we increase the sample size and decrease the variants of the drugs.

Step-by-step explanation:

In errors in statistics, we can define type I error as when the null hypothesis is rejected even when it is true while a type II error is when we fail to reject the null hypothesis even when it is false.

A) The null hypothesis in this question is that a drug is unsafe. Thus, the risk of committing Type I error would imply that an unsafe drug is approved. However, the risk of committing a Type II error would imply that a drug is safe but not approved.

B) The consumer groups feel that too many approved drugs are found out later to be unsafe. Thus, they don't want drugs that are unsafe to be approved and it means they are trying to avoid type I error.

C) The error that the Industry lobbyists are trying to avoid is the Type II error. This is because the companies would have to continue testing even when the drugs are safe.

D) To lower the chances of type I error, the significance level has to be reduced and they need to make sure that the tests are run for longer periods so that a good representation of the sample size would have been tested which means we are increasing the credibility of the test results.

To lower the chances s of type II error, we have to ensure we increase the sample size and decrease the variants of the drugs.

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: