Acetaminophen is an active ingredient found in more than 600 over-the-counter an

Question

Acetaminophen is an active ingredient found in more than 600 over-the-counter and prescription medicines, such as pain relievers, cough suppressants, and cold medications. It is safe and effective when used correctly, but taking too much can lead to liver damage.†

A researcher believes the amount of acetaminophen in a particular brand of cold tablets contains a mean amount of acetaminophen per tablet different from the 600 mg claimed by the manufacturer. A random sample of 36 tablets had a mean acetaminophen content of 597.2 mg with a standard deviation of 3.4 mg.

(a) Is the assumption of normality reasonable?

(b) Construct a 99% confidence interval for the estimate of the mean acetaminophen content. (Give your answers correct to two decimal places.)
___________to________ mg

(c) What does the confidence interval found in part (b) suggest about the mean acetaminophen content of one pill?

-The mean amount of acetaminophen in one pill may be 600 mg

.-The mean amount of acetaminophen in one pill is 600 mg exactly.     

-The mean amount of acetaminophen in one pill is more than 600 mg.

-The mean amount of acetaminophen in one pill is less than 600 mg.

Explanation / Answer

A. Yes, as n = 36 > 30, and the standard deviation is much less than the mean.

B. Using technology, using z distribution,

595.74 to 598.66 [using z]

or, using t,

595.66 to 598.74 [using t]

*****************

C.

Option D [answer]: The mean amount of acetaminophen in one pill is less than 600 mg. [D]

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