An aspirin manufacturer fills bottles by weight rather than by count. Since each

Question

An aspirin manufacturer fills bottles by weight rather than by count. Since each bottle must contain 100 tablets the average weight per tablet must be 5gr. One tablet from each bottle from a very large sample of bottles is weighed. The average weight of the sample was found to be 4.87gr with a (sample) standard deviation of 0.35gr. Is the information provided on a bottle’s label indicating that a bottle contains 100 tablets misleading? In this and in subsequent problems please don’t forget to state the assumptions you use in order to apply a specific hypothesis test or calculate a confidence interval as well as your final conclusion in layman’s language using formal English.

Explanation / Answer

The standard error of mean is:

Sm=root over s^2/n

=root over 0.35^2/100

=0.035

The 95% CI is:

x bar+/-t(0.95,99)*Smd/root over n

=4.87+/-1.984*0.035/10

=(4.86,4.87)

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