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

- September 24, 2021 /
- ecommerce Development, web development, Software Development, Online marketing, Magento, Ecommerce

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.

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?