Question

You work for the U.S. Food and Drug Administration. You have gotten word that a drug manufactoring is not accurately reporting the contents of their liquid cold medication. Under Federal Regulations, "Variations from stated quantity of contents shall not be unreasonably large" (see section q of the regulation by clicking here).

The company that produces the cold medication is claiming that each bottle contains 355 milliliters of cold medication, which is about 12 fluid ounces. In order to detemrine if they are accurate in their reporting, you decide to randomly select 20 different bottles of cold medication and measure the amount of cold medication in each bottle (in milliliters). The results of each sample are shown below.

Bottle Number	1	2	3	4	5	6	7	8	9	10
Milliliters	353	350	350	347	350	353	349	345	357	356

Bottle Number	11	12	13	14	15	16	17	18	19	20
Milliliters	351	343	344	351	347	343	354	360	347	352

a) Use the data shown above to construct a 93% confidence interval estimate for the mean amount of cold medication the company is putting in their bottles. Record the result below in the form of (#,#)(#,#). Round your final answer to two decimal places.


b) Is the company puting the claimed 355 milliliters of cold medication in their bottles? Explain.

• Yes, because 355 is inside of the confidence interval.
• Yes, because 355 is not inside the confidence interval.
• No, because 355 is inside the confidence interval.
• No, because 355 is not inside the confidence interval.

Answer 1

a)

sample mean 'x̄=	350.100
sample size   n=	20.00
sample std deviation s=	4.656
std error 'sx=s/√n=	1.0410

for 93% CI; and 19 df, value of t=		1.920
margin of error E=t*std error    =		1.999
lower bound=sample mean-E =		348.101
Upper bound=sample mean+E =		352.099

from above 93% confidence interval for population mean =(348.10 , 352.10)

b)

No, because 355 is not inside the confidence interval.