In Problem 3.69 on page 170, you were introduced to a tea-bag-filling operation. An important…

In Problem 3.69 on page 170, you were
introduced to a tea-bag-filling operation. An important quality characteristic
of interest for this process is the weight of the tea in the individual bags.
The file Teabags contains an ordered array of the weight, in grams, of a sample
of 50 tea bags produced during an 8-hour shift.

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In Problem 3.69 on page 170, you were introduced to a tea-bag-filling operation. An important…
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a. Is there evidence that the mean amount
of tea per bag is different from 5.5 grams? (Use  = 0.01.)

b. Construct a 99% confidence interval
estimate of the population mean amount of tea per bag. Interpret this interval.

c. Compare the conclusions reached in (a)
and (b).

Problem 3.69

A quality characteristic of interest for a
tea-bag-filling process is the weight of the tea in the individual bags. If the
bags are underfilled, two problems arise. First, customers may not be able to
brew the tea to be as strong as they wish. Second, the company may be in
violation of the truth-in-labeling laws. For this product, the label weight on
the package indicates that, on average, there are 5.5 grams of tea in a bag. If
the mean amount of tea in a bag exceeds the label weight, the company is giving
away product. Getting an exact amount of tea in a bag is problematic because of
variation in the temperature and humidity inside the factory, differences in
the density of the tea, and the extremely fast filling operation of the machine
(approximately 170 bags per minute). The file Teabags contains these weights,
in grams, of a sample of 50 tea bags produced in one hour by a single machine:

a. Compute the mean, median, first
quartile, and third quartile.

b. Compute the range, interquartile range,
variance, standard deviation, and coefficient of variation.

c. Interpret the measures of central
tendency and variation within the context of this problem. Why should the
company producing the tea bags be concerned about the central tendency and
variation?

d. Construct a boxplot. Are the data
skewed? If so, how?

e. Is the company meeting the requirement
set forth on the label that, on average, there are 5.5 grams of tea in a bag?
If you were in charge of this process, what changes, if any, would you try to
make concerning the distribution of weights in the individual bags?