An Introduction to Statistical Methods and Data Analysis
An Introduction to Statistical Methods and Data Analysis
7th Edition
ISBN: 9781305269477
Author: R. Lyman Ott, Micheal T. Longnecker
Publisher: Cengage Learning
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Chapter 1.6, Problem 3E

In 2014, Congress cut $8.7 billion from the Supplemental Nutrition Assistance Program (SNAP), more commonly referred to as food stamps. The rationale for the decrease is that providing assistance to people will result in the next generation of citizens being more dependent on the government for support. Hoynes (2012) describes a study to evaluate this claim. The study examines 60,782 families over the time period of 1968 to 2009 which is subsequent to the introduction of the Food Stamp Program in 1961. This study examines the impact of a positive and policy-driven change in economic resources available in utero and during childhood on the economic health of individuals in adulthood. The study assembled data linking family background in early childhood to adult health and economic outcomes. The study concluded that the Food Stamp Program has effects decades after initial exposure. Specifically, access to food stamps in childhood leads to a significant reduction in the incidence of metabolic syndrome (obesity, high blood pressure, and diabetes) and, for women, an increase in economic self-sufficiency. Overall, the results suggest substantial internal and external benefits of SNAP.

  1. a. Identify the population that is of interest to the researchers.
  2. b. Describe the sample.
  3. c. What characteristics of the population are of interest to the researchers?
  4. d. If the sample measurements are used to make inferences about the population characteristics, why is a measure of reliability of the inferences important?
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A well-known company predominantly makes flat pack furniture for students. Variability with the automated machinery means the wood components are cut with a standard deviation in length of 0.45 mm. After they are cut the components are measured. If their length is more than 1.2 mm from the required length, the components are rejected. a) Calculate the percentage of components that get rejected. b) In a manufacturing run of 1000 units, how many are expected to be rejected? c) The company wishes to install more accurate equipment in order to reduce the rejection rate by one-half, using the same ±1.2mm rejection criterion. Calculate the maximum acceptable standard deviation of the new process.
5. Let X and Y be independent random variables and let the superscripts denote symmetrization (recall Sect. 3.6). Show that (X + Y) X+ys.
8. Suppose that the moments of the random variable X are constant, that is, suppose that EX" =c for all n ≥ 1, for some constant c. Find the distribution of X.
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