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: 5.65 5.44 5.42 5.40 5.53 5.34 5.54 5.45 5.52 5.41 5.57 5.40 5.53 5.54 5.55 5.62 5.56 5.46 5.44 5.51 5.47 5.40 5.47 5.61 5.53 5.32 5.67 5.29 5.49 5.55 5.77 5.57 5.42 5.58 5.58 5.50 5.32 5.50 5.53 5.58 5.61 5.45 5.44 5.25 5.56 5.63 5.50 5.57 5.67 5.36 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?
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:
5.65 5.44 5.42 5.40 5.53 5.34 5.54 5.45 5.52 5.41
5.57 5.40 5.53 5.54 5.55 5.62 5.56 5.46 5.44 5.51
5.47 5.40 5.47 5.61 5.53 5.32 5.67 5.29 5.49 5.55
5.77 5.57 5.42 5.58 5.58 5.50 5.32 5.50 5.53 5.58
5.61 5.45 5.44 5.25 5.56 5.63 5.50 5.57 5.67 5.36
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?
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