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HTH 320 Midterm Exam: Statistics Questions and Answers, Exams of Statistics

James Madison University (JMU)Statistics

A comprehensive set of questions and answers covering key concepts in statistics, including descriptive and inferential statistics, scales of measurement, and research methods. it's particularly useful for students preparing for a midterm exam in a course like hth 320, offering a valuable review of fundamental statistical principles and their applications. The q&a format facilitates self-assessment and clarifies understanding of core statistical ideas.

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2024/2025

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HTH 320 MIDTERM EXAM QUESTIONS WITH COMPLETE

SOLUTIONS

statistics -- Answer ✔✔ mathematical procedures used to summarize, analyze, and

interpret observations

independent variable -- Answer ✔✔ •Those that are manipulated by the experimenter

•"Predictor"

dependent variable -- Answer ✔✔ •Those that are not under the experimenter's

control

•"Criterion"

frequency -- Answer ✔✔ •describes the number of times or how often a category,

score, or range of scores occurs

frequency distribution -- Answer ✔✔ -a summary display for a distribution of data

-an organized way to present data,

-showing the number of individuals located in each category on the scale of

measurement

-can be either a table or a graph

Partial preview of the text

Download HTH 320 Midterm Exam: Statistics Questions and Answers and more Exams Statistics in PDF only on Docsity!

HTH 320 MIDTERM EXAM QUESTIONS WITH COMPLETE

SOLUTIONS

statistics -- Answer ✔✔ mathematical procedures used to summarize, analyze, and interpret observations independent variable -- Answer ✔✔ •Those that are manipulated by the experimenter •"Predictor" dependent variable -- Answer ✔✔ •Those that are not under the experimenter's control •"Criterion" frequency -- Answer ✔✔ •describes the number of times or how often a category, score, or range of scores occurs frequency distribution -- Answer ✔✔ - a summary display for a distribution of data

an organized way to present data,
showing the number of individuals located in each category on the scale of measurement
can be either a table or a graph

always shows the categories that make up the scale, and the frequency, or number of individuals, in each category
to determine how many subjects were in the study, sum all the numbers in the frequency (f) column simple frequency distribution -- Answer ✔✔ summary display for:
the frequency of scores falling within defined groups or intervals (grouped data) in a distribution
generally more clear
the frequency of each individual score or category (ungrouped data) in a distribution grouped data -- Answer ✔✔ set of scores distributed into intervals, where the frequency of each score can fall into any one interval ungrouped data -- Answer ✔✔ - a set of scores or categories distributed individually, where the frequency for each individual score or category is counted
ungrouped when number of different scores is small, and for qualitative or categorical variables
to distribute, skip to final step for constructing a frequency distribution
not constructed/distributed into intervals interval -- Answer ✔✔ discrete range of values within which the frequency of a subset of scores is contained

add frequencies beginning from bottom and working up
top frequency equals total number of measures recorded proportions -- Answer ✔✔ Measures the fraction of the total group that is associated with each score
proportion= p= f/N
called relative frequencies because they describe the frequency ( f ) in relation to the total number (N) percentages -- Answer ✔✔ - expresses relative frequency out of 100
percentage = p(100) = f/N(100)
can be included as a separate column in a frequency distribution table relative frequency -- Answer ✔✔ Distributes the proportion of scores in each interval
equals the frequency in an interval divided by the total frequency count
often used to summarize large data sets relative percent -- Answer ✔✔ - distributes the percent of scores in each interval
multiple each relative frequency times 100
the sum of relative percents equals 100% cumulative relative frequency -- Answer ✔✔ - distributes the sum of relative frequencies across a series of intervals

can be summarized from bottom up or top down
the total sum of relative frequencies is equal to 1. cumulative percent -- Answer ✔✔ - distributes the sum of relative percents across a series of intervals
presented from bottom up; also called a percentile rank
total cumulative percent equal to 100%
a cumulative percent of scores from bottom up (shaded); also called percentile ranks. State whether a cumulative frequency, relative frequency, relative percent, cumulative relative frequency, or cumulative percent is most appropriate for describing the following situations. -- Answer ✔✔ Q:The frequency of businesses with at least 20 employees. A: Cumulative frequency (from the top down). Q: The frequency of college students with less than a 3.0 GPA. A: Cumulative frequency (from the bottom up). Q: The proportion of elderly patients consuming at or above 1,400 calories per day. A: Cumulative relative frequency (top down). percentile points and ranks -- Answer ✔✔ Identify individual rank by converting a frequency distribution to a cumulative percent distribution

datum (singular) -- Answer ✔✔ A single measurement or observation (commonly called a score or raw score) descriptive statistics -- Answer ✔✔ Used to summarize, organize, and simplify data.

summarize sample results Ex: Tables, graphs, averages inferential statistics -- Answer ✔✔ Allows sample results to be generalized to representative populations and interpret meaning of data
generalize to populations ex: common terms in inferential stats that you've probably heard- "statistically" and "practically significant" population -- Answer ✔✔ ENTIRE set of individuals or items of interest
data are termed "parameters", which are usually a numerical value that describe a population. (derived from measuring individuals in population.) sample -- Answer ✔✔ Representative subset of a population
data are termed "statistics", which are usually numeric and describe the sample. (derived from measuring individuals in the sample)
most behavioral research is done on samples research method -- Answer ✔✔ a set of systematic techniques used to acquire, modify, and integrate knowledge concerning observable and measurable phenomena

also known as scientific method
common research methods include experimental method, quasi-experimental method, and correlational method experimental method/design -- Answer ✔✔ The end goal is to demonstrate support for a CAUSAL relationship.
high level of control is needed to isolate cause and effect. Therefore, for a study to be considered an experiment, researchers must satisfy the following requirements.

Manipulation (of variables that operate in an experiment)
Randomization (of assigning participants to conditions)
Comparison/control Meeting experimental criteria -- Answer ✔✔ Requirement 1

must manipulate levels of an IV
IV --manipulated; the proposed cause
ex: effect of bold versus regular font on memory recall Requirement 2
random assignment renders group equivalent Requirement 3
at least two groups must be observed
DV -- what is measured; proposed effect

ex: what is the relationship between SAT scores (X) and freshman college GPA (Y)? scales of measurement -- Answer ✔✔ Degree to which measured variables conform to the abstract number system
determines the type of statistical analyses possible
includes: identity, order, equal distance, and absolute zero (i.e., complete absence of the variable)
popularly remembered by its acronym, NOIR Nominal -- Answer ✔✔ - categorical in nature
ex: gender, favorite color, seasons
does not imply any order among responses
ex: if i asked you all to tell me your favorite season (fall, winter, spring, summer), i couldn't put fall people ahead of spring people. Ordinal -- Answer ✔✔ - measurements that convey order or rank alone
allows us to see that one value is greater or less than another, but does not tell us meaningful info about the distance between levels
ex: order that you finished a race (first place, second place, third place)
ex: hospital rankings ("#1 U.S. cardio) interval (NOIR) -- Answer ✔✔ - numerical scales in which the intervals have the same interpretation throughout

ex: Fahrenheit temperature
no true zero point, even if the scale has an interval at zero
ex: zero degrees Fahrenheit does not represent that absence of temperature ratio -- Answer ✔✔ - ratio scales have all the properties of the interval scale, with the addition of a true zero (the zero position represents the absence of the quantity being measured)
ex: money... someone who has $50 has twice a much money as someone with $ continuous -- Answer ✔✔ measured along a continuum; measured at any place beyond the decimal point ex: Olympic sprinter's time to finish race discrete -- Answer ✔✔ Separate and indivisible categories; whole numbers only ex: socioeconomic class, amount of siblings quantitative -- Answer ✔✔ varies by amount qualitative -- Answer ✔✔ varies by form or class summation -- Answer ✔✔ - Summation is done after operations in parentheses, squaring, and multiplication or division.
Summation is done before other addition or subtraction

rectangles do not touch long the x-axis pie chart -- Answer ✔✔ summarizes the relative percent of discrete and categorical data into sectors
sector--represents the relative percent of a particular category central tendency -- Answer ✔✔ measures that tend to be toward the center of a distribution
a statistical measure
a single score to define the center of a distribution
used to locate a single score that is most representative or descriptive of all scores in a distribution
mean, median, and mode (types of c.t.)
differences in notation: population size is N; Sample size is n
purpose: find the single score that is most typical or best presents the entire group mean -- Answer ✔✔ Sum of a set of scores in a distribution, divided by the total number of scores summed
most commonly reported measure of central tendency
the "balance point" in a distribution
population mean: μ = Σx/N
sample mean= M = Σx/n

weighted mean -- Answer ✔✔ Combined mean of two or more groups of scores, where the number of scores in each group are unequal

often used when samples are of disproportionate size
Mw = Σ(M x n)/ n Characteristics of mean -- Answer ✔✔ 1. Changing an existing score will change the mean

Adding a new score or completely removing an existing score will change the mean, unless the value equals the mean •3. Adding, subtracting, multiplying, or dividing each score in a distribution by a constant will cause the mean to change by that constant •4. The sum of the differences of scores from their mean is zero •5. The sum of the squared differences of scores from their mean is minimal mean is reported for -- Answer ✔✔ Normal distributions of data

a normal distribution is a symmetrical distribution in which the mean, median, and mode all fall at the 50th percentile or center of the distribution
used because the mean includes all scores in its calculation Interval and ratio scale data
used because data on these scales can meaningfully convey information regarding differences between scores and their mean median -- Answer ✔✔ The middle value in a distribution of data listed in numeric order

Nominal scale data

nominal scale data represent something or someone; it is not a quantity
key phrases: most often, typical, or common central tendency in skewed distributions -- Answer ✔✔ - mean, influenced by extreme scores, is found far toward the long tail (positive or negative)
median, in order to divide scores in half, is found toward the long tail, but not as far as the mean
mode is found near the short tail.
if Mean - Median > 0, the distribution is positively skewed.
if Mean - Median < 0, the distribution is negatively skewed measure of variability -- Answer ✔✔ describe the distribution, particularly, how spread out the distribution is
measure how well an individual score represents the distribution
if there is little difference between the scores, a single value is informative
if there is a lot of difference between the scores, a single value is not so informative variability -- Answer ✔✔ - measure for the dispersion or spread of data in a distribution
a quantitative measure of the differences between scores
describes the degree to which the scores are spread out or clustered together
interval and ratio data are used

Ranges from 0 to + ∞
variability of scores can never be negative; scores can either not vary (variability is 0) or they can vary (variability is greater than 0)
as soon as one score differs from the others, there is variability range -- Answer ✔✔ Difference between the largest value (L) and smallest value (S) in a set of data
range = L - S
calculation only considers the largest and smallest value in the distribution
simplest way to describe the dispersion of scores
most informative for data without outliers
crude, unreliable measure of variability interquartile range (IQR) -- Answer ✔✔ •(IQR)--the 75th percentile minus the 25th percentile •Eliminating the top and bottom 25% of data rids data set of outliers •The location of the 1st quartile: (N+1)/ •The location of the 3rd quartile: 3*(N+1)/ semi-quartile range (SIQR) -- Answer ✔✔ - measure of half the distance between the cutoffs for the upper and lower quartiles of a data set
computed by dividing the IQR in half

standard deviation -- Answer ✔✔ Measure of variability for the average distance that scores deviate from their mean

calculated by taking the square root of the variance empirical rule -- Answer ✔✔ 1) at least 68% of all scores lie within one SD of the mean

at least 95% of all scores lie within two SD of the mean
at least 99.7% of all scores lie within three SD of the mean characteristics of standard deviation -- Answer ✔✔ 1. The SD is always positive

scores can either vary (greater than 0) or not vary (equal to 0)
a negative variability is meaningless

The SD is used to describe quantitative variables

SD is a numeric value and used to describe variables measured in numeric units

SD most informative when reported with the mean

reporting mean and SD can inform reader of distribution for close to all recorded data
reported as the mean plus or minus SD (M ± SD)

The value for the SD is affected by the value of every score in the distribution

adding or subtracting the same constant to each score will not change the value of the SD
multiplying or dividing each score using the same constant will cause the SD to change by that constant

if all the scores in a data set are the same, the SD is equal to... -- Answer ✔✔ ZERO. when all the scores are the same, they are all equal to the mean. Their deviations = 0, as does their Standard Deviation. characteristics of a normal distribution -- Answer ✔✔ 1) Normal distribution is mathematically defined

the shape of a normal distribution is specified by an equation relating each score (along x-axis) with each frequency (along y-axis)

Normal distribution is theoretical
Mean, median, and mode are all located at the 50th percentile
Normal distribution is symmetrical
The mean can equal any value
The standard deviation can equal any positive value purpose of z score -- Answer ✔✔ the number of standard deviations that X lies from μ on a standard scale. z = 0 ---> X = μ z > 0 ---> X > μ z < 0 ----> X < μ theoretical sampling -- Answer ✔✔ The order of selecting individuals matters and each individual selected is replaced before sampling again

to determine the number of samples of any size that can be selected from a population:

HTH 320 Midterm Exam: Statistics Questions and Answers, Exams of Statistics

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Partial preview of the text

Download HTH 320 Midterm Exam: Statistics Questions and Answers and more Exams Statistics in PDF only on Docsity!

HTH 320 MIDTERM EXAM QUESTIONS WITH COMPLETE

SOLUTIONS