What is a hypothesis?
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An educated guess based on observation.
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What is a hypothesis?
An educated guess based on observation.
What are the three types of variables based on their level of measurement?
Nominal, ordinal, or interval-ratio.
What are the real limits for the class interval 100-105?
99.5-105.5
What are the two types of variables based on their nature of values?
Discrete or continuous.
In a causal relationship, what is the term for the variable that represents the cause?
Independent variable
Give an example of an ordinal level variable.
Education level.
What happens if the empirical observation supports the hypothesis?
The hypothesis becomes a well-established theory.
What is the first step in the statistical process to help us understand phenomena?
Theory
What are continuous variables?
Variables measured in a unit that can be subdivided infinitely (fractional numbers).
What is the formula for calculating percentage?
% = (f / N) × 100
What are variables?
Traits that can change values from case to case, such as age, gender, race, and social class.
What does equal intervals mean in the context of interval-ratio variables?
It means that each unit increase represents the same amount, such as each child adding one unit.
What should always be reported along with proportions and percentages?
The number of observations.
What mathematical operations are permitted for nominal level measurements?
Counting number in each category, comparing sizes of categories.
What does f1 represent in the ratio formula?
f1 is the number of cases in the first category.
How is the birth rate calculated?
The birth rate is the number of births divided by the population size times 1000 per year.
What is the formula for calculating percentage change?
Percentage change = ((f2 - f1) / f1) × 100
How do frequency distributions summarize the distribution of a variable?
By reporting the number of times each score of a variable occurred.
What types of charts and graphs are used to present frequency distributions graphically?
Pie charts, bar graphs, histograms, and line charts.
Why are graphs and charts useful in data presentation?
They are very useful ways to display the overall shape of a distribution.
What does the line chart represent?
U.S. rates of marriage and divorce from 1950 to 2015 (rates per 100,000 population).
What are the real limits for the class interval 18-19?
17.5-19.5
What is the cumulative frequency for the age interval 20-21?
16
How do we observe the variables in the given example?
By looking at characteristics such as cute eyes, long hair, more muscle, and sexy body shape.
How does the statistical process help in understanding phenomena?
By moving from theory to hypothesis, then to observation, and finally to empirical generalization.
What is the first step in the empirical generalization process?
Get all possible data, in this case, everyone in Hong Kong.
What does the level of measurement refer to?
The mathematical quality of the scores of a variable.
What are interval-ratio variables?
Scores that are actual numbers and have a true zero point and equal intervals between scores.
What are the three characteristics that all variable categories should have?
Mutually exclusive, exhaustive, and homogenous.
Which religious affiliations are included in Scale D?
Protestant, Catholic, Jewish, None, Other.
What is the formula for a ratio?
Ratio = f1 / f2
What is the second step in calculating a ratio?
Divide f1 by f2.
What is the second step in calculating percentage change?
Subtract f1 from f2 (f2 - f1).
What are frequency distributions?
Tables that report the number of cases in each category of a variable.
For which type of variables are line charts especially appropriate?
Continuous interval-ratio level variables.
What are graphs and charts commonly used for in research?
Presenting 'pictures' of research results.
What is the y-axis representing in the histogram?
Percentage of total population.
What is the frequency of students who either disagree or strongly disagree that the University Health Center should provide condoms and other 'safe sex' items on demand and at no additional cost?
558
What is the midpoint of the class interval 3-5?
4.0
How many students are 18 years old in the ungrouped frequency distribution?
5 students.
How do you calculate the real limits from the stated limits?
Subtract 0.5 from the lower limit and add 0.5 to the upper limit.
What is the percentage change in population for the U.S. from 2018 to 2050?
18.78%
What is the frequency distribution of gender in the given data?
Males: 53, Females: 60, Total (N): 113
What is the frequency of people with other religious affiliations in the self-described religious affiliation of adult Americans in 2018 according to Table 2.2?
12,440,215
What follows the formulation of a theory in the statistical process?
Hypothesis
What is an ordinal level variable?
A variable where scores can be ranked from high to low or from more to less.
How do you compare a part to a whole in percentages and proportions?
By comparing a specific category (part) to all categories (whole).
How are theories and hypotheses often stated?
In terms of the relationships between variables.
What percentage of adult Americans identified as Protestant in 2018?
48.9%
For what levels of measurement can percentages and proportions be calculated?
Percentages and proportions can be calculated for variables at all levels of measurement.
What mathematical operations are permitted for ordinal level measurements?
All of the operations permitted for nominal level plus judgments of 'greater than' and 'less than'.
What is the ratio of males to females in a class of 23 females and 19 males?
19/23 = 0.83
What is the third step in calculating percentage change?
Divide by f1.
For which type of variables are histograms most appropriate?
Continuous interval-ratio level variables, but can also be used for discrete interval-ratio level variables.
What does it mean for categories in a frequency distribution to be exhaustive?
All possible cases must be included in the categories.
How is a pie chart divided?
Into segments which are proportional in size to the percentage of cases in each category.
How many students strongly disagree that the University Health Center should provide condoms and other 'safe sex' items on demand and at no additional cost?
210
How did the divorce rate change from 1950 to 2015?
The divorce rate increased until around 1980 and then gradually declined.
What does the sample bar chart compare?
Suicide rates for males and females by age group in 2017.
What is the midpoint of the class interval 9-11?
10.0
What is the percentage of students in the age interval 24-25?
5.0%
What is the total number of adult Americans surveyed for religious affiliation in 2018 according to Table 2.2?
253,881,929
What is the frequency of Muslims in the self-described religious affiliation of adult Americans in 2018 according to Table 2.3?
1,777,173
What is a frequency distribution for interval-ratio-level variables?
A frequency distribution for interval-ratio-level variables is a summary of data showing the number of occurrences within specified intervals or ranges of values.
What is the step after forming a hypothesis in the statistical process?
Observation
What type of survey items typically measure ordinal variables?
Survey items that measure opinions and attitudes, such as strongly disagree, disagree, neutral, agree, strongly agree.
What should be done after summarizing empirical evidence?
Decide whether the empirical observation supports the hypothesis.
What should be done if the empirical observation does not support the hypothesis?
Revise the theory according to the empirical observation.
What is the characteristic of interval-ratio level measurement?
Scores are numbers.
What does a true zero point mean in the context of interval-ratio variables?
It means that zero represents the absence of the variable being measured, such as 0 = no children.
How is race categorized as a nominal level variable?
1 = White, 2 = Black, 3 = Hispanic, 4 = Asian, 5 = Other.
What is the frequency of adult Americans who identified as Muslim in 2018?
1,777,173
What do ratios compare?
Ratios compare the relative sizes of categories.
What does a birth rate of 7.39 mean?
The town had 7.39 births for every 1000 residents.
What are line charts sometimes called?
Frequency polygons.
What type of limits do histograms use?
Real limits instead of stated limits.
What percentage of students strongly agree that the University Health Center should provide condoms and other 'safe sex' items on demand and at no additional cost?
25.55%
What was the percentage of adult Americans identifying as Protestant in 2018?
48.90%
What are the stated limits for the class interval 18-19?
18-19
What are the real limits for the class interval 3-5?
2.5-5.5
What is the cumulative percentage for the age interval 22-23?
90.0%
What is the interval width for the grouped frequency distribution of student ages?
2 years of age.
What is the midpoint of the class interval 118-123?
120.5
What is the percentage change in population for Mexico from 2018 to 2050?
25.61%
What additional religious groups are included in Table 2.3 that are not in Table 2.2?
Muslim and Buddhist
What is the theory to be tested in the example?
Is it easier for good-looking people to find a couple than those who are ordinary in appearance?
What is the purpose of drawing a sample in empirical research?
To gather data from a subset of the population, such as 100 men.
In percentages and proportions, what is the denominator?
The whole (all categories).
What is the characteristic of ordinal level measurement?
Scores have some numerical quality and can be ranked.
What does it mean for variable categories to be homogenous?
Each category should be similar in nature.
How is political party categorized as a nominal level variable?
1 = Republican, 2 = Democrat, 3 = Other.
What are examples of ordinal level measurements?
Social class, attitude and opinion scales.
What mathematical operations are permitted for interval-ratio level measurements?
All of the operations permitted for nominal and ordinal levels plus all other mathematical operations (addition, subtraction, multiplication, division, square roots, etc.).
If a town of 2300 had 17 births last year, what is the birth rate?
(17 / 2300) * 1000 = 7.39
What was the murder rate in a state by 2000?
10.7
What must be decided when creating frequency distributions for interval-ratio level variables?
The number of categories and the width of those categories.
What does it mean for categories in a frequency distribution to be mutually exclusive?
Each case is counted in one and only one category.
What percentage of students disagree that the University Health Center should provide condoms and other 'safe sex' items on demand and at no additional cost?
25.40%
What was the percentage of adult Americans identifying as having no religion in 2018?
23.30%
What do cumulative frequencies and percentages refer to?
They refer to how many cases fall below a given score or class interval.
Which age group has the highest suicide rate for males according to the chart?
75 and older.
How are the suicide rates measured in the chart?
Rates of suicide per 100,000 in each age group.
How many students are aged 20-21 in the grouped frequency distribution?
5 students.
What is the projected population change for Mexico from 2018 to 2050?
33,500,000
What is the frequency of Jewish individuals in the self-described religious affiliation of adult Americans in 2018 according to Table 2.2?
4,315,993
What are the two types of variables based on their role in an experiment?
Independent or dependent.
What is the final step in the statistical process that leads to understanding phenomena?
Empirical Generalization
Give an example of a discrete variable.
Number of children or number of cars.
In percentages and proportions, what is the numerator?
The part (specific category).
What is the formula for calculating proportion?
Proportion = f / N
In the formulas for percentage and proportion, what does 'N' represent?
The number of cases in all categories
What does it mean for variable categories to be exhaustive?
All possible options should be included.
Which religious affiliations are included in Scale A?
Protestant, Episcopalian, Catholic, Jewish, None, Other.
What measurement procedures are used for nominal level measurements?
Classification into categories.
What are examples of interval-ratio level measurements?
Age, number of children, income.
What is the first step in calculating a ratio?
Determine the values of f1 (the number of cases in category 1) and f2 (the number of cases in category 2).
What is the formula to calculate the birth rate?
(Number of births / Population size) * 1000
In the percentage change formula, what does f2 represent?
f2 represents the second score, frequency, or value.
What do histograms look like?
They look like bar charts.
What does the histogram in the image represent?
The age distribution of the United States in 2017.
What is the frequency of students who agree that the University Health Center should provide condoms and other 'safe sex' items on demand and at no additional cost?
462
What percentage of students either strongly agree or agree that the University Health Center should provide condoms and other 'safe sex' items on demand and at no additional cost?
59.27%
What is the midpoint of the class interval 0-2?
1.0
How many students are in the age interval 18-19?
11
What is the midpoint of the class interval 112-117?
114.5
What is the total number of students in the grouped frequency distribution?
20 students.
What is the projected population change for Canada from 2018 to 2050?
12,700,000
What is the next step after collecting data in empirical research?
Summarize empirical evidence.
In the formulas for percentage and proportion, what does 'f' represent?
Frequency, or the number of cases in any category
What are nominal level variables?
Scores that are different from each other but cannot be treated as numbers.
Which religious affiliations are included in Scale B?
Protestant, Catholic, Jewish, None, Other.
How many adult Americans identified as having no religious affiliation in 2018?
59,154,489
What does f2 represent in the ratio formula?
f2 is the number of cases in the second category.
How many females are there for every male in a class of 23 females and 19 males?
1.21 females
What was the murder rate in a state in 1990?
7.3
What is the relative change in the murder rate from 1990 to 2000?
46.58%
Can line charts be used for discrete interval-ratio level variables?
Yes, they can be used for discrete interval-ratio level variables.
What is the range of age groups displayed in the histogram?
0-5 years to 85 years and older.
How did the marriage rate change from 1950 to 2015?
The marriage rate showed a general decline from 1950 to 2015, with some fluctuations.
What are the stated limits for the class interval 3-5?
3-5
What is the midpoint of the class interval 100-105?
102.5
What is the cumulative frequency for the age interval 26-27?
20
What is the projected population change for Nigeria from 2018 to 2050?
214,700,000
What is the frequency of people with no religious affiliation in the self-described religious affiliation of adult Americans in 2018 according to Table 2.2?
59,154,489
What are discrete variables?
Variables measured in units that cannot be subdivided (whole numbers).
What is the characteristic of nominal level measurement?
Scores are labels only, they are not numbers.
What does the term 'case' refer to?
The entity from which data are gathered, such as people, groups, states, and nations.
Can nominal level variables be treated as numbers?
No, they are just labels and cannot be treated as numbers.
What should you report when dealing with a small number of cases (less than 20)?
Report actual frequencies.
Which religious affiliations are included in Scale C?
Protestant, Non-Protestant.
What is the total number of adult Americans surveyed for religious affiliation in 2018?
253,881,927
What type of comparison do ratios make?
Ratios compare parts to parts.
What is the first step in calculating percentage change?
Determine the values for f1 (the value at time 1) and f2 (the value at time 2).
What are the basic considerations for frequency distributions for interval-ratio level variables?
Complexity, large number of scores, requires collapsing or grouping of categories, deciding the number of categories and the width of those categories.
What is a general rule for categories of frequency distribution?
Categories must be exhaustive and mutually exclusive.
How do the categories (or scores) of the variable appear in a histogram?
The categories (or scores) of the variable border each other, meaning the sides of the bars touch.
What do the heights of the bars in a bar chart represent?
The number or percentage of cases in each category.
What is a midpoint in the context of class intervals?
The point exactly halfway between the upper and lower limits of a class interval.
What was the trend in divorce rates around the 1980s?
Divorce rates peaked around 1980 and then began to decline.
What are the stated limits for the class interval 100-105?
100-105
What is the percentage change in population for China from 2018 to 2050?
-3.58%
In which age group is the difference between male and female suicide rates the most significant?
75 and older.
What is the cumulative percentage for the age interval 24-25?
95.0%
What is the percentage change in population for Canada from 2018 to 2050?
34.14%
What is the hypothesis in the given example?
Guys with more muscle tend to use less time to secure a romantic date.
In a causal relationship, what is the term for the variable that represents the effect?
Dependent variable
What does reporting relative size involve?
Comparing the number of cases in a specific category to the number of cases in all categories.
What is an example of an interval-ratio variable?
Age (in years).
What does it mean for variable categories to be mutually exclusive?
Each category should be distinct with no overlap.
What percentage of adult Americans identified as Jewish in 2018?
1.7%
What measurement procedures are used for ordinal level measurements?
Classification into categories plus ranking of categories with respect to each other.
What does percentage change measure?
The relative increase or decrease in a variable over time.
Why might collapsing or grouping of categories be required in frequency distributions for interval-ratio level variables?
Because of the large number of scores.
By what percentage did the murder rate increase from 1990 to 2000?
46.58%
What type of variables are bar charts useful for?
Discrete variables.
What is the total number of responses in the survey about support for birth control on a university campus?
1370
What was the percentage of adult Americans identifying as 'Other' in 2018?
4.90%
What can be inferred about the relationship between marriage and divorce rates over time?
As marriage rates declined, divorce rates initially increased but then also started to decline.
Which age group has the highest suicide rate for females according to the chart?
45 to 64.
What is the projected population change for the U.S. from 2018 to 2050?
61,600,000
What percentage of students are aged 22-23 in the grouped frequency distribution?
10.0%.
What is the frequency of Protestants in the self-described religious affiliation of adult Americans in 2018 according to Table 2.2?
124,148,263
What is the frequency of people with other religious affiliations in the self-described religious affiliation of adult Americans in 2018 according to Table 2.3?
8,631,985
What is the relationship between an independent variable and a dependent variable in a causal relationship?
The independent variable causes changes in the dependent variable.
Give an example of a continuous variable.
Age or income.
What is an example of an interval-ratio variable related to family size?
Number of children.
How can graphs be used to present data?
Graphs can be used to present data visually, making it easier to identify patterns, trends, and relationships within the data.
What are examples of nominal level measurements?
Gender, race, religion, marital status.
What percentage of adult Americans identified with religions other than Protestant, Catholic, Jewish, Muslim, or Buddhist in 2018?
3.4%
How many males are there for every female in a class of 23 females and 19 males?
0.83 males
What is the fourth step in calculating percentage change?
Multiply by 100.
How do you calculate the relative change in the murder rate from 1990 to 2000?
(10.7 - 7.3) / 7.3 * 100
What are class intervals in the context of frequency distributions?
Class intervals refer to the categories used in the frequency distribution.
What is the source of the data used in the histogram?
U.S. Bureau of the Census, 2018. American Community Survey, 2013-2017, Five Year Estimates.
What was the percentage of adult Americans identifying as Catholic in 2018?
21.20%
How do you calculate the midpoint of a class interval?
Add the upper limit to the lower limit and divide by 2.
What is the interval width for the ungrouped frequency distribution of student ages?
1 year of age.
What is the projected population change for China from 2018 to 2050?
-49,900,000
What is the midpoint of the class interval 106-111?
108.5
What is the total number of students in the class?
20
What is the projected population change for the U.K. from 2018 to 2050?
8,300,000
What is the frequency of Buddhists in the self-described religious affiliation of adult Americans in 2018 according to Table 2.3?
2,031,055
Give an example of an interval-ratio variable related to income.
Income (in dollars).
Give an example of a nominal level variable for sex.
1 = Female, 2 = Male.
How many adult Americans identified as Catholic in 2018?
53,822,969
What percentage of adult Americans identified as Buddhist in 2018?
0.8%
What measurement procedures are used for interval-ratio level measurements?
All of the procedures used for nominal and ordinal levels plus description of scores in terms of equal units.
What is the optional third step in calculating a ratio?
Multiply by a power of 10.
What is the ratio of females to males in a class of 23 females and 19 males?
23/19 = 1.21
In the percentage change formula, what does f1 represent?
f1 represents the first score, frequency, or value.
How are line charts constructed similarly to histograms?
By graphing a dot at each category’s midpoint and then connecting the dots.
What type of variables are pie charts useful for?
Discrete variables with only a few categories.
What does each segment in a pie chart represent?
The percentage of cases in each category.
What was the percentage of adult Americans identifying as Jewish in 2018?
1.70%
What was the trend in marriage rates around the 1970s?
Marriage rates peaked around the early 1970s before starting to decline.
What is the midpoint of the class interval 6-8?
7.0
What is the total number of students in the ungrouped frequency distribution?
20 students.
Which age group has the lowest suicide rate for both males and females?
10 to 14.
Which nation has the highest projected percentage change in population from 2018 to 2050?
Nigeria (109.60%)
What is the percentage change in population for the U.K. from 2018 to 2050?
12.50%
What percentage of students are aged 18-19 in the grouped frequency distribution?
55.0%.
What is the cumulative percentage for the age interval 18-19?
55.0%
What is the frequency of Catholics in the self-described religious affiliation of adult Americans in 2018 according to Table 2.2?
53,822,969
What are some basic concepts of statistics?
Basic concepts of statistics include understanding data types, measures of central tendency, measures of variability, and the principles of statistical inference.
What are ratios, rates, and percentage change used for in statistics?
Ratios, rates, and percentage change are used to compare different quantities, measure the occurrence of events over time, and quantify the relative change between two values, respectively.
How can percentages and proportions enhance clarity in data presentation?
Percentages and proportions can enhance clarity by providing a relative measure of frequency, making it easier to compare different categories or groups.
What is a frequency distribution for ordinal-level variables?
A frequency distribution for ordinal-level variables is a summary of data showing the number of occurrences of each category, where the categories have a meaningful order.
What is a frequency distribution for nominal-level variables?
A frequency distribution for nominal-level variables is a summary of data showing the number of occurrences of each distinct category.
