Question

1. A quality characteristic of interest for a tea-bag 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 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. 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 tea, and the extremely fast filling operation of machine (approximately 170 bags per minute). Here is the sample of 50 tea bags produced in an 8-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 null hypothesis

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

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

use in excel if possible

Answer 1

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