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POSC 202A
Fall 2015
Homework #1
In general, for the math questions you will want to show as much work as possible. Ideally, you will use graph paper but you can use regular notebook paper if you want to be difficult. For the R-based questions, and exercises from Zuur et al, you can use a mix a
Due 10/14
Moore and McCabe: Questions:
1.2, 1.54, 1.62, 1.74, 3.2, 3.52, 3.54, 3.67 3.70
In R:
What is a package/library in R? How do you install a package?
What is a function? What is an argument?
What is a working directory? Why is it important? What is a text editor?
Zuur et al (Note: Consider using HYPERLINK "http://www.statmethods.net/" http://www.statmethods.net/ for some of these)
2.4 Exercise 1 Exercise 7 (Data available here: http://www.highstat.com/book3.htm)
1.54. See also the solution to Exercise 1.37. (a) The mean of this distribution appears to be higher than 100. (There is no substantial difference between the standard deviations.)
(b) The mean and median are quite similar; the mean is slightly smaller due to the slight left skew of the data. (c) In addition to the mean and median, the standard deviation is shown for reference (the exercise did not ask for it).
Note: Students may be somewhat puzzled by the statement in (b) that the median is
close to the mean (when they differ by 1.1), followed by (c) where they differ a bit
(when M " x = 0.382). It may be useful to emphasize that we judge the size of such
differences relative to the spread of the distribution. For example, we can note that 1.1
13.17
.=
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2.1
.=
0.18 for (c).
x s M
IQ 108.9 13.17 110
GPA 7.447 (2.1) 7.829
1.62. Note that estimates for (a) and (b) will vary. (a) The median would be in position
14,959+1/2 = 7480 in the list; from the boxplot, we estimate it to be about $45,000. (b) The
quartiles would be in positions 3740 and 11,220, and we estimate their values to be about $32,000 and $65,000. (c) Omitting these observations should have no effect on the median and quartiles. (The quartiles are computed from the entire set of data; the extreme 5% are omitted only in locating the ends of the lines for the boxplot.)
Note: The positions of the quartiles were found according to the texts method; that is,
these are the locations of the medians of the first and second halves of the list. Students
might instead compute 0.25 14, 959 and 0.75 14, 959 to obtain the answers 3739.75 and 11,219.25.
1.74. (a) x = 5.4479 and s = 0.2209. (b) The first measurement corresponds to
5.50 62.43 = 343.365 pounds per cubic foot. To find xnew and snew, we similarly multiply by 62.43: xnew
.=
340.11 and snew .= 13.79.
Note: The conversion from cm to feet is included in the multiplication by 62.43; the
step-by-step process of this conversion looks like this:
(1 g/cm3)(0.001 kg/g)(2.2046 lb/kg)(30.483 cm3/ft3) = 62.43 lb/ft3
3.2. The anecdote describes a single unusual event. We would like data on deaths and injuries for occupants wearing/not wearing restraints for many accidents.
3.6. (a) In this observational study, we do not know if the reduction in heart attack risk was due to hormones or other factors. An experiment would have involved taking a (very large) group of women, splitting them randomly into two groups; one would take hormones, and the other would not. The random allocation would allow us to conclude that, if we observed a difference in heart attack risk in either group, it could be attributed to the treatment.
(b) Possible characteristics might include socio-economic factors; for example, women who take hormones might be wealthier and therefore have better access to health care. There might also be biological factors; perhaps women who are more sensitive to menopause (and are therefore more likely to use hormones to relieve its symptoms) are also at less risk for heart attacks.
3.52. Each student has a 10% chance: 3 out of 30 over-21 students, and 2 of 20 under-21 students. This is not an SRS because not every group of 5 students can be chosen; the only possible samples are those with 3 older and 2 younger students.
3.54. The higher no-answer was probably the second periodmore families are likely to be gone for vacations, and so on. Nonresponse of this type might underrepresent those who are more affluent (and are able to travel). In general, high nonresponse rates always make results less reliable, because we do not know what information we are missing.
3.67. (a) The sample size for Hispanics was smaller. Smaller sample sizes give less
information about the population, and therefore lead to larger margins of error (with the
same confidence level). (b) The sample size was so small, and the margin of error so large, that the results could not be viewed as an accurate reflection of the population of Cubans.
3.70. (a) The population is Ontario residents; the sample is the 61,239 people interviewed.
(b) The sample size is very large, so if there were large numbers of both sexes in the
samplethis is a safe assumption because we are told this is a random samplethese two numbers should be fairly accurate reflections of the values for the whole population.
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