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Chapter 7: Q 1RP. (page 310)
Define sampling error?
When an analyst fails to select a sample that accurately represents the entire population of data, a sampling mistake occurs.
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Ethanol Railroad Tariffs. An ethanol railroad tariff is a fee charged for shipments of ethanol on public railroads. The Agricultural Marketing Service publishes tariff rates for railroad-car shipments of ethanol in the Biofuel Transportation Database. Assuming that the standard deviation of such tariff rates is , determine the probability that the mean tariff rate of randomly selected railroad car shipments of ethanol will be within of the mean tariff rate of all railroad-car shipments of ethanol. Interpret your answer in terms of sampling error.
According to The Earth: Structure, Composition and Evolution for earthquakes with a magnitude of 7.5 or greater on the Richter scale, the time between successive earthquakes has a mean of 437 days and a standard deviation of 399 days. Suppose that you observe a sample of four times between successive earthquakes that have a magnitude of7.5 or greater on Richter scale.
Part (a): On average, what would you expect to be the mean of the four times?
Part (b): How much variation would you expect from your answer in part (a)?
America's Riches. Each year, Forbes magazine publishes a list of the richest people in the United States. As of September l6, 2013, the six richest Americans and their wealth (to the neatest billion dollars) are as shown in the following table. Consider these six people a population of interest.
(a) For sample size of construct a table similar to table 7.2 on page293 what is the relationship between the only possible sample here and the population?
(b) For a random sample of size determine the probability that themean wealth of the two people obtained will be within (i.e, billion) of the population mean. interpret your result in terms of percentages.
Refer to Exercise 7.6 on page 295.
a. Use your answers from Exercise 7.6(b) to determine the mean, , of the variable for each of the possible sample sizes.
b. For each of the possible sample sizes, determine the mean, , of the variable , using only your answer from Exercise 7.6(a).
7.47 Baby Weight. The paper "Are Babies Normal?" by T. Clemons and M. Pagano (The American Statistician, Vol. 53, No, 4. pp. 298-302) focused on birth weights of babies. According to the article, the mean birth weight is grams ( pounds, ounces) with a standard deviation of 581 grams.
a. Identify the population and variable.
b. For samples of size , find the mean and standard deviation of all possible sample mean weights.
c. Repeat part (b) for samples of size.
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