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Chapter 1: Q 2. (page 31)
Almost any inferential study involves aspects of descriptive statistics. Explain why.
To organize any summarised information collected from a sample, descriptive statistics are used in inferential studies.
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Comparing Gas Mileages. An experiment is to be conducted to compare four different brands of gasoline for gas mileage.
(a) Suppose that you randomly divide 24 cars into four groups of 6 cars each and then randomly assign the four groups to the four brands of gasoline, one group per brand. Is this experimental design a completely randomized design or a randomized block design? If it is the latter, what are the blocks?
(b) Suppose, instead, that you use six different models of cars whose varying characteristics (e.g., weight and horsepower) affect gas mileage. Four cars of each model are randomly assigned to the four different brands of gasoline. Is this experimental design a completely randomized design or a randomized block design? If it is the latter, what are the blocks?
(c) Which design is better, the one in part (a) or the one in part (b)? Explain your answer.
Explain why a census is often not the best way to obtain information about a population.
Genocide. The document "American Attitudes about Genocide" provided highlights of a nationwide poll with 1000 participants. The survey, conducted by Penn Schoen Berland between June 30 and July 10, 2012, revealed that "66% of respondents believe that genocide is preventable."
(a). Is the statement in quotes an inferential or a descriptive statement? Explain your answer.
(b). Based on the same information, what if the statement had been "66% of Americans believe that genocide is preventable"?
Persistent Poverty and IQ. An article appearing in an issue of the Arizona Republic reported on a study conducted by G. Duncan of the University of Michigan. According to the report, "Persistent poverty during the first 5 years of life leaves children with IQs 9.1 points lower at age 5 than children who suffer no poverty during that period...." Is this statistical study an observational study or is it a designed experiment? Explain your answer.
In Exercises 1.92-1.97, we present descriptions of designed experiments. In each case, identify the
(a) experimental units
(b) response variable
(c) factor (s)
(d) levels of each factor:-
(e) treatments.
The Lion's Mane. In a study by P. M. West titled "The Lion's Mane" ( American Scientist, Vol. 93, No. 3, pp. 226-236), the effects of the mane of a male lion as a signal of quality to mates and rivals was explored. Four life-sized dummies of male lions provided a tool for testing female response to the unfamiliar lions whose manes varied by length (long or short) and color (blonde or dark). The female lions were observed to see whether they approached each of the four life-sized dummies.
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