An Introduction to Statistical Methods and Data Analysis
An Introduction to Statistical Methods and Data Analysis
7th Edition
ISBN: 9780357670620
Author: R. Lyman Ott; Micheal T. Longnecker
Publisher: Cengage Learning US
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Chapter 1.6, Problem 6E

An American history professor at a major university was interested in knowing the history literacy of college freshmen. In particular, he wanted to find what proportion of college freshmen at the university knew which country controlled the original 13 colonies prior to the American Revolution. The professor sent a questionnaire to all freshman students enrolled in HIST 101 and received responses from 318 students out of the 7,500 students who were sent the questionnaire. One of the questions was “What country controlled the original 13 colonies prior to the American Revolution?”

  1. a. What is the population of interest to the professor?
  2. b. What is the sampled population?
  3. c. Is there a major difference in the two populations. Explain your answer.
  4. d. Suppose that several lectures on the American Revolution had been given in HIST 101 prior to the students receiving the questionnaire. What possible source of bias has the professor introduced into the study relative to the population of interest?
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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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