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1. A quality characteristic of interest for a tea-bag fillingprocess is the weight of the tea in the individual bags. In thisexample, the label weight on the package indicates that the meanamount is 5.5 grams of tea in a bag. If the bags are underfilled,two problems arise. First, customers may not be able to brew thetea to be as strong as they wish. Second, the company may be inviolation of the truth-in-labeling laws. On the other hand, if themean amount of tea in a bag exceeds the label weight, the companyis giving away product. Getting an exact amount of tea in a bag isproblematic because of variation in the temperature and humidityinside the factory, differences in the density of tea, and theextremely fast filling operation of machine (approximately 170 bagsper minute). Here is the sample of 50 tea bags produced in an8-hour shift

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

a. What is the Null and alternative Hypothesis

b. What are the n and the d.f for this problem

c.What test and formula should use to test the nullhypothesis

d. is there evidence that the mean amount of tea per bag isdifferent from 5.5 grams per bag (use σ = .01)

e. Construct a 99% confidence interval estimate for thepopulation mean weight of the tea bags. Interpret this interval

use in excel if possible