Problem 1.

The file Energy contains the per capita energy consumption, in kilowatt-hours, for each of the 50 states and the District of Columbia during a recent year.

a. Compute the mean, variance, and standard deviation for the population.

b. What proportion of these states has per capita energy consumption within ± 1 standard deviation of the mean, within ± 2 standard deviations of the mean, and within ± 3 standard deviations of the mean?

c. Compare your findings with what would be expected based on the empirical rule. Are you surprised at the results in (b)?

d. Repeat (a) through (c with the District of Columbia removed. How have the results changed?

Problem 2.

A quality characteristic of interest for a teabag filling process is the weight of the tea in the individual bags. 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. 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 the 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, the range, the interquartile range, variance, standard deviation, and the coefficient of variation of the sample data.

b. 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?

c. Construct a boxplot. Are the data skewed? If so, how?

d. 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?

Problem 1. The file Energy contains the per capita energy consu...