Chapter 1 Statistical And Critical Thinking (b) Math

Question 1

Amount the 1038 surveyed adults, 52 said that secondhand smoke is “not harmful.” What is the percentage of people who chose “ not at all harmful”?

Answer 1

52
— = .05
1038

Question 2

A voluntary response sample ( or self selected sample) is one in which the respondents themselves decide whether to be included.

Answer 2

You have a survey either internet or radio or in the ‘email.
Question: had radio survey, did i call in, no. This is an example of a voluntary response. Because if it is a radio survey, first of all, and you are only reaching people that are listening to that particular station. Not only that but then you are only going get responses from the people who are near a phone or it is convenient to call as well as the fact that if you don’t feel strongly about something, you likely will not respond. And usually, to feel strong, it is a negative feeling. And so you are getting a very, very skewed result there when you are using a radio survey.

Question 3

Small samples. Conclusions should not be based on samples that are far too small.

Answer 3

An example: we have would be the children’s defense fund. They published something called children out of school in America. What they said was that out of children who had been suspended in one region, sixty - seven percent of those that were suspended: they were suspended at least three times. But, up that there were only three children in that region that they were surveying. Meaning you are only looking at three children of two9 third of the means only two kids was suspended two time, meaning it still a verify small number

Question 4

Graphs, such as bar graph and pie charts, can be used to exaggerate or understate the true nature of data.

Question 5

a parameter

Answer 5

A parameter is a numerical measurement describing some characteristic of a
population.
.

Question 6

a statistic

Answer 6

A statistic is a numerical measurement describing some characteristic of a
sample.

Question 7

hint

Answer 7

HINT The alliteration in “population parameter” and “sample statistic” helps us
remember the meanings of these terms.

Question 8

parameter example

Answer 8

1. Parameter: The population size of 250,342,875 adults is a parameter,
   because it is the entire population of all adults in the United States. (If we
   somehow knew the percentage of all 250,342,875 adults who have a credit
   card, that percentage would also be a parameter.)

Question 9

statistic example

Answer 9

2. Statistic: The sample size of 1659 adults is a statistic, because it is based on a
   sample, not the entire population of all adults in the United States. The value
   of 28% is another statistic, because it is also based on the sample, not on the
   entire population

Question 10

quantitative or numerical

Answer 10

Quantitative (or numerical) data consist of numbers representing counts or
measurements.

Question 11

categorical or qualitative

Answer 11

Categorical (or qualitative or attribute) data consist of names or labels (not
numbers that represent counts or measurements).

Question 12

nomnresponse

Answer 12

Nonresponse A nonresponse occurs when someone either refuses to respond to
a survey question or is unavailable. When people are asked survey questions, some
firmly refuse to answer. The refusal rate has been growing in recent years, partly be-cause many persistent telemarketers try to sell goods or services by beginning with a
sales pitch that initially sounds as though it is part of an opinion poll. (This “selling
under the guise” of a poll is called sugging.) In Lies, Damn Lies, and Statistics, author
Michael Wheeler makes this very important obse

Question 13

quantitative caterical

Answer 13

Categorical EXAMPLE 2
1. Quantitative Data: The ages (in years) of subjects enrolled in a clinical trial
2. Categorical Data as Labels: The genders (male>female) of subjects
enrolled in a clinical trial
3. Categorical Data as Numbers: The identifcation numbers 1, 2, 3, . . . , 25
are assigned randomly to the 25 subjects in a clinical trial. Those numbers
are substitutes for names. They don’t measure or count anything, so they are
categorical data

Question 14

discrete,continuous

Answer 14

Discrete,Continuous
Quantitative data can be further described by distinguishing between discrete and con-tinuous types.

Question 15

discrete data

Answer 15

Discrete data result when the data values are quantitative and the number of
values is finite, or “countable.” (If there are infinitely many values, the collection of
values is countable if it is possible to count them individually, such as the number
of tosses of a coin before getting tails.)

Question 16

continous (numerical) data

Answer 16

Continuous (numerical) data result from infinitely many possible quantitative
values, where the collection of values is not countable. (That is, it is impossible
to count the individual items because at least some of them are on a continuous
scale, such as the lengths of distances from 0 cm to 12 cm.)

Question 17

discrete data of the infinite type

Answer 17

2. Discrete Data of the Infinite Type: A statistics student plans to toss a fair
   coin until it turns up heads. It is theoretically possible to toss the coin for-ever without ever getting heads, but the number of tosses can be counted,
   even though the counting could go on forever. Because such numbers
   result from a counting procedure, the numbers are discrete.

Question 18

discrete data of the finite type

Answer 18

Discrete Data of the Finite Type: A statistics professor counts the number
of students in attendance at each of her classes. The numbers are discrete
because they are fnite numbers resulting from a counting process.

Question 19

continous data

Answer 19

Continuous Data: Burmese pythons are invading Florida. Researchers
capture pythons and measure their lengths. So far, the largest python captured
in Florida was 17 feet long. If the python lengths are between 0 feet and 17
feet, there are infnitely many values between 0 feet and 17 feet. Because it is
impossible to count the number of diferent possible values on such a continu-ous scale, these lengths are continuous data.

Question 20

example gramma fewer vs less

Answer 20

GRAMMAR: FEWER VERSUS LESS When describing smaller amounts, it is correct
grammar to use “fewer” for discrete amounts and “less” for continuous amounts. It is
correct to say that we drank fewer cans of cola and that, in the process, we drank less
cola. The numbers of cans of cola are discrete data, whereas the volume amounts of
cola are continuous data.

Question 21

nominal level

Answer 21

The nominal level of measurement is characterized by data that consist of
names, labels, or categories only. The data cannot be arranged in some order
(such as low to high).

Question 22

nominal level example

Answer 22

Here are examples of sample data at the nominal level of measurement.
1. Ye s,No,
Undecided: Survey responses of yes, no, and undecided
2. Coded Survey Responses: For an item on a survey, respondents are given a
choice of possible answers, and they are coded as follows: “I agree” is coded
as 1; “I disagree” is coded as 2; “I don’t care” is coded as 3; “I refuse to
answer” is coded as 4; “Go away and stop bothering me” is coded as 5. The
numbers 1, 2, 3, 4, 5 don’t measure or count anything

Question 23

ordinal level of measurement

Answer 23

Data are at the ordinal level of measurement if they can be arranged in some
order, but differences (obtained by subtraction) between data values either cannot be
determined or are meaningless

Question 24

Ordinal Level

Answer 24

Ordinal Level EXAMPLE 5
Here is an example of sample data at the ordinal level of measurement.
Course Grades: A college professor assigns grades of A, B, C, D, or F. These
grades can be arranged in order, but we can’t determine differences between the
grades. For example, we know that A is higher than B (so there is an ordering), but
we cannot subtract B from A (so the difference cannot be found).

Question 25

interval level of measurement

Answer 25

Data are at the interval level of measurement if they can be arranged in order, and differences between data values can be found and are meaningful. Data at the interval level do not have a natural zero starting point at which none of the quantity is present.

Question 26

Interval Level example

Answer 26

Interval Level EXAMPLE 6 These examples illustrate the interval level of measurement. 1. Temperatures: The lowest and highest temperatures recorded on earth are -129°F and 134°F. Those values are examples of data at the interval level of mea-surement. Those values are ordered, and we can determine that their diference is 263°F. However, there is no natural starting point. The value of 0°F is arbitrary and does not represent the total absence of heat (negative temperatures are common). 2. Years: The years 1492 and 1776 can be arranged in order, and the difer-ence of 284 years can be found and is meaningful. However, time did not begin in the year 0, so the year 0 is arbitrary instead of being a natural zero starting point representing “no time.” The years of 1492 and 1776 are therefore at the interval level of measurement. 3. Shoe Sizes: The shoe sizes of 10 and 5 can be arranged in order, and the dif-ference is the same as the diference in shoe sizes of 8 and 13. However, size 0 is arbitrary.

Question 27

ratio level of measurement

Answer 27

Data are at the ratio level of measurement if they can be arranged in order, differ-ences can be found and are meaningful, and there is a natural zero starting point (where zero indicates that none of the quantity is present). For data at this level, differences and ratios are both meaningful

Question 28

ratio level

Answer 28

Ratio Level EXAMPLE 7 The following are examples of data at the ratio level of measurement. Note the presence of the natural zero value, and also note the use of meaningful ratios of “twice” and “three times.” 1. Heights of Students: Heights of 180 cm and 90 cm for a high school student and a preschool student (0 cm represents no height, and 180 cm is twice as tall as 90 cm.) 2. Class Times: The times of 50 min and 100 min for a statistics class (0 min represents no class time, and 100 min is twice as long as 50 min.) YOUR TURN. Do

Question 29

ratio level

Answer 29

Ratio Level EXAMPLE 7 The following are examples of data at the ratio level of measurement. Note the presence of the natural zero value, and also note the use of meaningful ratios of “twice” and “three times.” 1. Heights of Students: Heights of 180 cm and 90 cm for a high school student and a preschool student (0 cm represents no height, and 180 cm is twice as tall as 90 cm.) 2. Class Times: The times of 50 min and 100 min for a statistics class (0 min represents no class time, and 100 min is twice as long as 50 min.) YOUR TURN. Do

Question 30

hint, tatio test focus on the term ratio and true zero for ratios to make sense

Answer 30

HINT The distinction between the interval and ratio levels of measurement can be a bit tricky. Here are two tools to help with that distinction: 1. Ratio Test Focus on the term “ratio” and know that the term “twice” describes the ratio of one value to be double the other value. To distinguish between the interval and ratio levels of measurement, use a “ratio test” by asking this question: Does use of the term “twice” make sense? “Twice” makes sense for data at the ratio level of measurement, but it does not make sense for data at the interval level of measurement. 2. True Zero For ratios to make sense, there must be a value of “true zero,” where the value of zero indicates that none of the quantity is present, and zero is not simply an arbitrary value on a scale. The temperature of 0°F is arbitrary and does not indicate that there is no heat, so temperatures on the Fahrenheit scale are at the interval level of measurement, not the ratio level

Question 31

Terabytes

Answer 31

Terabytes (10^12 or 1,000,000,000,000 bytes) of data

Question 32

Petabytes

Answer 32

■ ■Petabytes (10^15 bytes) of data

Question 33

exabytes

Answer 33

■ ■Exabytes (10^18 bytes) of data

Question 34

zettabytes

Answer 34

■ ■Zettabytes (10^21 bytes) of data

Question 35

yottabytes

Answer 35

■ ■Yottabytes (10^24 bytes) of data

Question 36

missing com pletely at radom

Answer 36

A data value is missing completely at random if the likelihood of its being miss-ing is independent of its value or any of the other values in the data set. That is, any data value is just as likely to be missing as any other data value.

Question 37

missing not at random

Answer 37

A data value is missing not at random if the missing value is related to the reason that it is missing

Question 38

placebo

Answer 38

A placebo is a harmless and ineffective pill, medicine, or procedure sometimes used for psychological benefit or sometimes used by researchers for comparison to other treatments.

Question 39

experiment

Answer 39

In an experiment, we apply some treatment and then proceed to observe its effects on the individuals. (The individuals in experiments are called experimental units, and they are often called subjects when they are people.)

Question 40

Frequency Distributions Histograms Graphs That Enlighten and Graphs That Deceive

Answer 40

Frequency Distributions for Organizing and Summarizing Data * Develop an ability to summarize data in the format of a frequency distribution and a relative frequency distribution. * For a frequency distribution, identify values of class width, class midpoint, class lim-its, and class boundaries. 2-2 Histograms * Develop the ability to picture the distribution of data in the format of a histogram or relative frequency histogram. * Examine a histogram and identify common distributions, including a uniform distribu-tion and a normal distribution. 2-3 Graphs That Enlighten and Graphs That Deceive * Develop an ability to graph data using a dotplot, stemplot, time-series graph, Pareto chart, pie chart, and frequency polygon. * Determine when a graph is deceptive through the use of a nonzero axis or a picto-graph that uses an object of area or volume for one-dimensional data.

Question 41

Lower class limits upper class limits class boundaries class midpoint class width

Answer 41

Lower class limits are the smallest numbers that can belong to each of the differ-ent classes. (Table 2-2 has lower class limits of 0, 15, 30, 45, 60, 75, and 90.) Upper class limits are the largest numbers that can belong to each of the different classes. (Table 2-2 has upper class limits of 14, 29, 44, 59, 74, 89, and 104.) Class boundaries are the numbers used to separate the classes, but without the gaps created by class limits. Figure 2-1 on the next page shows the gaps created by the class limits from Table 2-2. In Figure 2-1 we see that the values of 14.5, 29.5, 44.5, 59.5, 74.5, and 89.5 are in the centers of those gaps. Following the pattern of those class boundaries, we see that the lowest class boundary is -0.5 and the highest class boundary is 104.5. The complete list of class boundaries is -0.5, 14.5, 29.5, 44.5, 59.5, 74.5, 89.5, and 104.5. Class midpoints are the values in the middle of the classes. Table 2-2 has class midpoints of 7, 22, 37, 52, 67, 82, and 97. Each class midpoint can be found by adding the lower class limit to the upper class limit and dividing the sum by 2. Class width is the difference between two consecutive lower class limits (or two con-secutive lower class boundaries) in a frequency distribution. Table 2-2 uses a class width of 15. (The first two lower class limits are 0 and 15, and their difference is 15.)

Question 42

boston commute time boston commute time refer relative frequency distribution

Answer 42

Boston Commute Time The accompanying table summarizes daily commute times in Boston. How many commute times are included in the summary? Is it possible to identify the exact values of all of the original data amounts? 2. Boston Commute Time Refer to the accompanying frequency distribution. What problem would be created by using classes of 0–30, 30–60, . . . , 120–150? 3. Relative Frequency Distribution Use percentages to construct the relative frequency dis-tribution corresponding to the accompanying frequency distribution for daily commute time in Boston.

Question 43

histogram

Answer 43

A histogram is a graph consisting of bars of equal width drawn adjacent to each other (unless there are gaps in the data). The horizontal scale represents classes of quantitative data values, and the vertical scale represents frequencies. The heights of the bars correspond to frequency values

Question 44

important Uses of a Histogram

Answer 44

important Uses of a Histogram ■ ■Visually displays the shape of the distribution of the data ■ ■Shows the location of the center of the data ■ ■Shows the spread of the data ■ ■Identifies outliers