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Nature of Mathematics
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Chapter 14 / Exercise 24
Nature of Mathematics
Smith
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Chapter 1 1a) Population: All American households Sample: The 953 American households that were surveyed 1b) Population: All Thomas Nelson students Sample: The 200 randomly selected Thomas Nelson students 2a) parameter (describes a population; census is a survey of entire population) 2b) statistic (describes a sample) 3a) quantitative, continuous (measured) 3b) qualitative (not a number) 3c) quantitative, discrete (whole numbers) 3d) qualitative (even though it’s a number, it’s ju st a label) 4a) systematic 4b) stratified (grouping things into “strata” by common characteristic and then sampling from each strata to get a representative sample) 4c) cluster (selecting a few natural groups) 4d) stratified 4e) simple random 4f) convenience 5a) sampling and nonresponse; members of women’s groups are not necessarily representative of women as a whole and there were many people who did not respond to the survey it’s possible that the only people who responded had very strong opinions about the issue and people with more moderate opinions were underrepresented. Should try to reach a broader audience (not just women’s groups), and possibly use call - backs or incentives to get more responses. 5b) response bias; people may not give their honest opinions about the police when being asked face-to-face by a police officer. Should make it so people will not be afraid to express their true opinions; perhaps a written or electronic anonymous survey or at least not being surveyed by uniformed police officers themselves. 5c) sampling bias, possibly nonresponse; this is a convenience sample since they are just asking the people watching their tv show and having a toll is going to discourage most people from responding. Should conduct a survey through a proper random sampling method and not have a cost to respond. 5d) sampling bias; subscribers of time magazine are not representative of all Americans. Should conduct a survey through a proper random sampling method and not just survey magazine subscribers. 5e) non-response; way too few responses to get a representative sample. Could try call-backs or incentives, or maybe a method other than a mail questionnaire (possibly phone calls or electronic surveys), to try to get more responses. 6a) ob servational (observed, didn’t try to influence) 6b) observational (observed, didn’t try to influence) 6c) designed experiment (experimenter controlled which treatment each subject would get)
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Nature of Mathematics
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Chapter 14 / Exercise 24
Nature of Mathematics
Smith
Expert Verified
7a) Lurking variable: wealth. Homeowners probably have more money to afford medical treatments and a healthy lifestyle. 7b) Lurking variable: time. Those people probably would have gotten over their cold in 2 weeks with no treatment. 8) Showing two variables have a correlation (positive correlation meaning that high values of one variable are associated with high values of another variable; negative correlation meaning that high values of one variable are associated with low values of another variable) does not mean that we can conclude that one variable causes the other variable to change. Even if the correlation is shown statistically to be very strong and one

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