A quality characteristic of interest for a teabag filling process is the weight of the tea in the individual bags. In this example, the label weight on the package indicates that the mean amount is 5.5 grams of tea in a bag. If the bags are under filled, 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. On the other hand, 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 following data are the weights, in grams, of a sample of 50 tea bags produced in one hour by a single machine:
5.65 5.445.425.405.535.34 5.54 5.45 5.52 5.41
5.57 5.405.535.545.555.62 5.56 5.46 5.44 5.51
5.47 5.405.475.615.535.32 5.67 5.29 5.49 5.55
5.77 5.575.425.585.585.50 5.32 5.50 5.53 5.58
5.61 5.455.445.255.565.63 5.50 5.57 5.67 5.36
a. Construct a 99% confidence interval estimate for the population mean weight of the tea bags.
b. Is the company meeting the requirement set forth on the label that the mean amount of tea in a bag is 5.5 grams?
c. Do you think the assumption needed to construct the confidence interval estimate in (a) is valid?