Stats Midterm ALL
What is the median for the following set of scores? Scores: 1, 2, 5, 6, 17
it is 5
quasi-independent variable
"Independent variable" used to create nonexperimental groups
For a population with σ = 10, a score that is located 20 points above the mean would have a z-score of ____.
(+2)
probability of A =
(Number of outcomes classified as A)/(total possible outcomes)
how to find semi interquartile range
(Q3-Q1)/2
z score formula
(X-μ)/σ
weighted mean
(ΣX1+ΣX2)/(n1+n2)
range for extreme scores 12 to 3
10 (12.5 - 2.5)
A jar contains 40 red marbles and 10 black marbles. If you take a random sample of n = 3 marbles from this jar, and the first two marbles are both red, what is the probability the third marble will be black?
10/50
A jar contains 10 red marbles and 20 blue marbles. If you randomly select one marble from the jar, what is the probability of getting a red marble?
10/thirty
A normal distribution has a mean of μ = 36 with σ = 4. What proportion of the distribution consists of scores between X = 34 and X = 38?
2(0.1915) = 0.3830
What proportion of a normal distribution is located between z = +0.50 and z = −0.50?
2(0.1915) = 0.3830
What proportion of a normal distribution is located between z = +1.00 and z = −1.00?
2(0.3413) = 0.6826
A sample of n = 5 scores produces SS = 20. The variance for this sample is ____.
20/4 = 5
A population of n = 5 scores produces SS = 20. The variance for this population is ____.
20/5 = 4
in the class interval 40-49, the real limits are
39.5 to 49.5
variable
A characteristic or condition that changes or has different values for different individuals
In a hypothesis test using a t statistic, what is the influence of using a large sample?
A larger sample tends to increase the likelihood of rejecting the null hypothesis.
variability
A quantitative measure of the degree to which scores in a distribution are spread out or clustered together
sample
A set of individuals selected from a population, usually intended to represent the population in a research study, The people whom you study
Statistics
A set of mathematical procedures for organizing, summarizing, and interpreting Information, Condenses large quantities of info into a few simple figures
datum
A singular measurement or observation
central tendency
A statistical measure to determine a single score that defines the center of a distribution.
Symmetrical Distribution
A symmetrical graph
Parameter
A value, typically numerical, that describes a population
statistic
A value, typically numerical, that describes a sample
A random sample is selected from a population with μ = 80 and σ = 20. Which of the following samples would have an expected value of M equal to 80?
All of the samples would have an expected value of 80.
frequency distribution
An organized tabulation of the number of individuals located in each category on the scale of measurement, Takes a disorganized set of scores and places them in order from highest to lowest, grouping together all individuals who have the same score, Shows whether the scores are high or low, concentrated in one area or spread out across the entire scale, provides organized pic of data\
standard deviation
Approximates the average distance from the mean
One item on a questionnaire asks, "How many siblings (brothers and sisters) did you have when you were a child?" A researcher computes the mean, the median, and the mode for a set of n = 50 responses to this question. Which of the following statements accurately describes the measures of central tendency?
Because the scores are all whole numbers, the mode will be a whole number.
nominal scale
Categories with different names but that are related to each other in a systemic way, Race, gender, occupation, etc, No quantitative distinctions
participant variables
Characteristics such as age, gender, intelligence - vary from individual to another, Researchers must assure that these are consistent across the board
population variance
SS/N = (E(X - μ)^2/N)
Graph Shape
Defined by an equation that prescribes the exact relationship between each x and y value on the graph
the best way to divide up grouped frequency distribution
Determine the range of scores, Subtract the smallest X value from the largest, Determine what interval size would provide ~10 rows
To calculate EX is frequency distributions...
EfX
The critical boundaries for a hypothesis test are z = +1.96 and -1.96. If the z-score for the sample data is z = -1.90, then what is the correct statistical decision?
Fail to reject H 0.
bar graph
For nominal/ordinal data (non-numerical), Spaces between adjacent bars
goal of the median
Goal is to determine the midpoint of the distribution
Relative Frequencies
Graph does not show absolute values, but instead relative number of one category to the other
grouped frequency distribution
Groups presented instead of scores, Class intervals
Operational Definition
Identifies a measurement procedure (set of operations) for measuring an external behavior and uses the resulting measurements as a definition and a measurement of a hypothetical construct
What does it mean to say that the sample variance is an unbiased statistic?
If many different samples are selected, the average of the sample variances will be equal to the population variance.
If two samples are selected from the same population, under what circumstances will the two samples have exactly the same t statistic?
If the samples are the same size and have the same mean and have the same sample variance
Smooth Curves
Indicates no connecting of dots (real frequencies), Shows relative changes
Continuous Variable
Infinite number of possible values that fall between two values, Divisible into an infinite number of fractional parts, For any two points on a line, it is always possible to find a third between them
constructs
Internal attributes/characteristics that cannot be directly observed, useful for describing/explaining behavior
environmental variables
Lighting, time of day, weather
nonequivalent group study
Like boys vs girls, No real control over preexisting groups
histogram
List the numerical scores (categories of measurement along x axis), Frequency on y axis. Adjacent bars touch, no gaps, Can add // to represent a large gap in categories/numerical values
how to find interquartile range
Locate the boundary that separates the top 25% of the distribution (third Quartile), Locate the boundary that separates the bottom 25% (first quartile) , Subtract Q1 from Q3
LRL for Xmin
Lower Real Limit for Xmin (if score is 45, Xmin is 44.5)
In a sample of n = 6, five individuals all have scores of X = 10 and the sixth person has a score of X = 16. What is the mean for this sample?
M = 11
A sample of n = 4 individuals is obtained from a population with μ = 80. Which set of sample statistics would produce the most extreme value for t?
M = 88 and s2 = 8
A researcher uses a hypothesis test to evaluate H 0 μ = 80. Which combination of factors is most likely to result in rejecting the null hypothesis?
M = 90 and n = 20
A sample of n = 25 scores was obtained from a population with μ = 80. Which of the following sets of sample statistics will produce the most extreme value for the t statistic?
M = 90 and s2 = 10
A researcher uses a hypothesis test to evaluate H 0 μ= 80. Which combination of factors is most likely to result in rejecting the null hypothesis?
M = 90 and α = .05
A researcher uses a hypothesis test to evaluate H 0 μ = 80. Which combination of factors is most likely to result in rejecting the null hypothesis?
M = 90 and σ = 10
t stat formula
M-μ/SM
population variance
Mean squared deviation, average squared distance from the mean
Central Tendency
Measures where the center of the distribution is
sample variance
SS/df
variance
SS/n
Ef =
N
A population with a mean of μ = 8 has ∑ X = 40. How many scores are in the population?
N = 5
pre-post study
No control over the passage of time
control condition
No experimental treatment
Polygons
Numerical scores (categories of measurement) along x axis, Center a dot above each score that corresponds to frequency, Draw continuous line from dot to dot, Draw line down to x axis at value 1 less than lowest measured, Can be used for grouped distribution, Position dot above midpoint of class interva
the correlational method
Observe two variables as they exist naturally for a set of individuals, determine if there's a relationship between the two, Simply measure the two variables (Scatter plot), Shows a clear relationship between the variables (Chi-square test)
what is the purpose/role of statistics
Organize and summarize information so that researchers can see what happened in the research study and can communicate results, Help the researcher to answer the general questions that initiated the research by determining what conclusions are justified based on results
raw scores
Original, unchanged scores that are a direct result of measurement
experimental condition
Receive experimental treatment
A researcher conducts a hypothesis test to evaluate the effect of a treatment. The hypothesis test produces a z-score of z = −2.60. Assuming that the researcher is using a two-tailed test, what is the correct statistical decision?
Reject the null hypothesis with either α = .05 or α = .01.
symbol for estimated standard error
SM
how is estimated standard error typically computed
SM = sqrt(s^2/n)
sample variance
SS/(n-1)
SS definitional formula
SS=E(X-μ)^2
SS computational formula
SS=EX^2-[(EX)^2/N]
A population has a mean of μ = 100 and a standard deviation of σ = 20. Which of the following random samples is least likely to be obtained?
Sample mean of M = 104 from a sample of size n =100.
Skewed Distribution
Scores tend to pile up toward one end of the scale and taper off gradually at the other
Discrete Variable
Separate, indivisible categories, No values can exist between categories, Whole, countable numbers, Number of family members, students in a class, etc.
Interval/Ratio Scale
Series of ordered categories (like an ordinal scale), Equidistant from one another, Interval - Arbitrary zero point 0 assigned to a particular location on the scale simply as a matter of convenience/reference (Fahrenheit scale) Ratio - 0 point not arbitrary but meaningful at representing none of the variable being (Height, weight) Numbers reflect ratios of magnitude
Ordinal Scale
Set of categories organized in an ordered sequence, Ranked in size or magnitude (1st, 2nd, 3rd, etc or Small, medium, large) Used when it's difficult to assign numerical scores
Tail
Side where graph tapers off
modified histogram
Stack of blocks instead of a bar, No y axis necessary
descriptive statistics
Statistical procedures used to summarize, organize, and simplify data, Techniques that take raw scores and organize/summarize in a more manageable form (Table/graph, Average), Simplifies data
Negative Skew
Tail points toward the negative
Positive Skew
Tail points toward the positive
inferential statistics
Techniques that allow us to study samples and then make generalizations about the populations from which they were selected, Interprets data, Researchers use sample stats as the basis for conclusions about population parameters
Variability
Tells whether the scores are spread over a wide range or are clustered together
degrees of freedom
The degrees of freedom determine the number of scores in the sample that are independent and free to vary.
range
The difference between the URL of Xax and LRL Xmin
sampling error
The discrepancy/amount of error that exists between a sample statistic and the corresponding population parameter, "Margin of error", The natural differences that exist, by chance, between a sample statistic and a population parameter
Law of Large Numbers
The larger the sample size (n), the more probable it is that the sample mean will be close to the population mean
interquartile range
The range covered by the middle 50% of the distribution (Q3-Q1)
mode
The score or category that has the greatest frequency
median
The score that divides the distribution in half so that 50% of the individuals in the distribution have scores at or below the median.
population
The set of all the individuals of interest in a particular study, The group you want to generalize results about
mean
The sum of the scores divided by the number of scores
nonexperimental research
Two variables are still compared, yet without manipulation
URL for Xmax
Upper Real Limit for Xmax (if score is 45, Xmax is 45.5)
independent variable
Variable manipulated by researcher, Antecedent conditions manipulated prior to observing dependent, ALWAYS AT LEAST 2 VALUES (manipulated, not manipulated, for comparison)
why use median with undetermined values
We can't calculate ΣX for the mean
why use median with extreme scores/skewed scores
When a distribution has a few extreme scores, then the mean may not be a good representative of the majority Because it is relatively unaffected by extreme scores, median is commonly used when reporting average value for skewed distribution
Graphs for Population Distribution
When you can obtain exact frequency for each score in a population
deviation calculation
X - μ
Scores on the SAT form a normal distribution with μ = 500 and σ = 100. What is the minimum SAT score needed to be in the top 10% of the distribution?
X = 628
For a normal distribution with μ = 100 and σ = 10, what scores ( X values) separate the middle 95% from the rest?
X = 80.4 and X = 119.6
deviation score
X-μ
formula for X in terms of z-score
X=μ+zσ
Which of the following is a major difference between a hypothesis test with the t statistic formula and the test with a z-score?
You must calculate the sample variance (or standard deviation) for the t statistic but not for the z-score., You must know the population variance (or standard deviation) for the z-score but not for the t statistic., You use the unit normal table to find critical values for the z-score test but not for the t test.
z-score formula for finding probability associated with sepcific sample mean
Z = (M-μ)/σM
in words, the t formula is
[(sample mean from data)-(population mean hypothesized from null)]/estimated standard error computer from the sample data
What kind of frequency distribution graph shows the frequencies as bars that are separated by spaces?
a bar graph
data set
a collection of measurements or observations
Sampling Distribution
a distribution of statistics obtained by selecting all possible samples of a specific size from a population
Which set of sample characteristics is most likely to produce a significant t statistic?
a large sample size and a small sample variance
A Type I error means that a researcher has ____.
concluded that a treatment has an effect when it really has no effect
A sample of n = 16 individuals is selected from a population with μ = 80 and a treatment is administered to the sample. After treatment, the sample mean is M = 84 and the sample variance is s 2 = 100. If Cohen's d is used to measure effect size for this study, what value will be obtained for d?
a measly 0.40
the bottom score in each class interval should be
a multiple of the width
Instead of showing the actual number of individuals in each category, a population frequency distribution graph usually shows ____.
a relative frequency
what should the width of each class interval be
a relatively simple number (2, 5, 10)
A sample is obtained from a population with μ =100 and σ = 20. Which of the following samples would produce the z-score closest to zero?
a sample of n = 25 scores with M = 102
The normal distribution is an example of _____________.
a smooth curve showing data from a population
Hypothesis Test
a statistical method that uses sample data to evaluate a hypothesis about a population
A researcher reports a t statistic with df = 20. Based on this information, how many individuals were in the sample?
a whopping 21
x axis
abscissa
on average, the sample variances produce an ____ estimate of population variance
accurate, unbiased
One basic assumption is made about the effect of the treatment: if the treatment has any effect, it is simply to
add a constant amount to each individual's score
The value for the standard deviation is determined by ____.
all of the scores in the distribution
the distribution of sample means contains...
all possible samples
control
an aspect of the experimental method, control over the research situation to ensure that no other variables affect outcome
manipulation
an aspect of the experimental method, manipulation of one variable, observation of another
estimated standard error
an estimate of the real standard error σM when the value of σ is unknown. It is computed from the sample variance or sample standard deviation and provides an estimate of the standard distance between a sample mean M and the population mean μ
A researcher risks a Type I error ____.
anytime H 0 is rejected
in the class interval 40-49, 40-49 are the
apparent limits
in symmetrical distributions, the mean, mode, and median...
are all the same (the middle of the graph)
how many class intervals should a grouped frequency distribution have
around 10
where should the sampling distribution pile up
around the population mean
A Type II error means that a researcher has ____.
concluded that a treatment has no effect when it really does
Normal curve
bell curve
sample variability gives a ____ estimate of population variability
biased
major mode
bigger mode
In a study evaluating the effectiveness of a new medication designed to control high blood pressure, one sample of individuals is given the medicine and a second sample is given a placebo. Blood pressure is measured for each individual. For this study, what is the dependent variable?
blood pressure
real limits
boundaries of intervals for scores that are represented on a continuous number line
step 3 t stat
calculate the t score
central tendency of sampling distribution
centered around mean of population
step 4 t stat
compare t score to critical region
what's the problem with the range
completely ignores middle scores, doesn't give an accurate description of variability for entire distributions
A variable that has an infinite number of possible values between any two specific measurements is called a(n) ____ variable.
continuous
As sample size increases, the standard error of M ____.
decreases
as sample size increases, the standard error...
decreases
degrees of freedom
describe the number of scores in a sample that are independent and free to vary. Because the sample mean places a restriction on the value of one score in the sample, there are n-1 degrees of freedom for the sample
Statistical techniques that summarize, organize, and simplify data are classified as ____.
descriptive statistics
4 steps to calculating standard deviation
determine deviation for each individual score (x - μ), square each deviation (X - μ)^2, find the variance (mean of squared deviations, E(X - μ)^2/N), square root of variance sqrt(E(X - μ)^2/N)
zσ is the _____ of X
deviation
the t stat forms a ratio between
diff between sample data and pop hypothesis and how much difference is reasonable to expect between sample mean and population mean
a standardized distribution is used to make _____ distributions_______
dissimilar, comparable
deviation
distance from the mean
the goal of statistical research is to
draw conclusions about the population
cohen's d measures
effect size
If the tail of a normal distribution contains exactly 2.5% of the scores, then what is the z-score value that separates the tail from the body of the distribution?
either z = 1.96 or z = -1.96
For a perfectly symmetrical distribution with μ = 30, the median would have a value ____.
equal to 30
the average of the sample means is _____ to the population mean
exactly equal
when to use the median
extreme scores/skewed scores, undetermined values, open-ended distributions, ordinal scales
percentage for each score p(100) =
f(100)/N
proportion (relative frequency) for each score p =
f/N
A sample of n = 5 scores has SS = 20. The variance for this sample is 4. t/f
false.
A vertical line drawn through a normal distribution at z = −2.00 will separate the distribution into two sections. The proportion in the smaller section is 0.9772. t/f
false.
A vertical line is drawn through a normal distribution so that exactly 75.80% of the distribution is on the left-hand side of the line. The line was drawn at z = 0.80. t/f
false.
Adding a new score to a distribution will always change the value of the mean. t/f
false.
Although the size of the sample can influence the outcome of a hypothesis test, it has little or no influence on measures of effect size. t/f
false.
For a two-tailed test with α = .05 and a sample of n = 25, the boundaries for the critical region are t = ±2.060. t/f
false.
For any population, a z-score of +1.00 corresponds to a location exactly 10 points above the mean. t/f
false.
If all other factors are held constant, increasing the sample size from n = 25 to n = 100 will increase the power of a statistical test. t/f
false.
If other factors are held constant, then increasing the sample standard deviation will increase the likelihood of rejecting the null hypothesis. t/f
false.
In a frequency distribution graph, the frequency values are presented on the horizontal axis and the scores (or measurement categories) are presented on the vertical axis. t/f
false.
In general, an increase in the sample variance makes it more likely that the t statistic will be large enough to reject the null hypothesis. t/f
false.
It is possible for a distribution to have more than one mean. t/f
false.
Measures of effect size, such as r2 or Cohen's d, are not greatly influenced by sample variance. t/f
false.
On a 100-point test, you have a score of X = 73. Based on this information, you know that you definitely scored above the median.
false.
Statistical procedures that attempt to organize and summarize data are classified as inferential statistics. t/f
false.
The standard error for a sample mean can never be larger than the standard deviation of the population from which the sample is selected. t/f
false.
There is enough information in a grouped frequency distribution table to obtain a complete listing of the original set of scores. t/f
false.
To find ∑Χ for the scores in a frequency distribution table, you simply add the values in the X column. t/f
false.
For the past 20 years, the high temperature on April 15th has averaged μ = 62 degrees with a standard deviation of σ = 4. Last year, the high temperature was 72 degrees. Based on this information, last year's temperature on April 15th was ____.
far above average
A z-score of z = +3.00 indicates a location that is ____.
far above the mean in the extreme right-hand tail of the distribution
the primary use of distribution of sample means is to...
find probability associated with any specific sample
For a normal distribution with μ = 500 and σ = 100, what score separates the top 40% of the distribution from the rest?
five two five (525)
Central Limit Theorem
for any population with mean μ and standard deviation σ, the distribution of sample means for sample size n will have a mean of μ and a standard deviation of σ√n, and will approach a normal distribution as n approaches infinity
A sample of n = 5 scores has SS = 40. If the same five scores were a population, then the value obtained for the population SS would be ____.
forty (40)
In a population with μ = 60, a score of X = 58 corresponds to a z-score of z = −0.50. What is the population standard deviation?
four (4)
f
frequencies column heading
research starts with a
general question about the population
One sample of n = 4 scores has a mean of M = 10, and a second sample of n = 8 scores has a mean of M = 20. If the two samples are combined, the mean for the combined sample will be ____.
greater than 15 but less than 20
semi interquartile range
half the interquartile range
the real limit separating two adjacent scores is ________
halfway between them
in a frequency distribution, how are the categories listed
highest to lowest (nominal in any order)
in a z score, the number specifies ...
how far away the score is from the mean in terms of standard deviations
a hypothesis test starts with a ____ about a _____
hypothesis, population
Sample variance provides an unbiased estimate of the population variance. The term unbiased means ____.
if sample variance is computed for many samples, the average sample variance will equal the population variance
when is the sample statistc biased
if the average value for a sample statistic consistently underestimates or overestimates the corresponding population parameters
Statistical methods that use sample data to answer general questions about a population are called ____.
inferential statistics
sample-> _____ -> population
inferential statistics
purpose of inferential statistics
interpret data
To determine the size of the difference between two measurements, a researcher must use a(n) ____ scale of measurement.
interval or ratio
when measuring a continuous variable, each measurment cateogry should is an ____ defined by _____
interval, boundaries
when a continuous variable is measured, the resulting measurements correspond to
intervals as opposed to single points
When n is small (less than 30), the t distribution ____.
is flatter and more spread out than the normal z distribution
A set of N = 20 exam scores has a mean of μ = 50. The instructor discovered that an error was made grading one exam, so 20 points are added to that student's score. After adding the 20 points, what is the new mean for the class?
it is 51
What is the mean for the following scores? Scores: 1, 4, 13
it is 6
What proportion of a normal distribution is located between z = 1.00 and z = 1.50?
it's 0.0919
A random sample of n = 4 scores is selected from a normally distributed population with μ = 80 and σ = 12. What is the probability that the sample mean will be greater than 86?
it's 0.1587
A sample of n = 25 individuals is selected from a population with μ = 60 and σ = 10 and a treatment is administered to the sample. After treatment, the sample mean is M = 63. What is the value of Cohen's d for this sample?
it's 0.30
What is the probability of randomly selecting from a normal distribution a z-score that is greater than z = −0.80 ?
it's 0.7881
A sample of n = 4 scores has SS = 48. What is the variance for this sample?
it's 16
For any normal distribution, the percentile rank for z = 0.50 is ____.
it's 69.15%
If random samples, each with n = 9 scores, are selected from a normal population with μ = 80 and σ = 18, and the mean is calculated for each sample, then the average of all the sample means would be ____.
it's 80
A distribution is normal and has μ = 90 and σ = 10. What is the 64th percentile?
it's 93.6
A sample of n = 4 scores has SS = 48. What is the estimated standard error for this sample?
just 2
Xmax
largest score
to find the median when n is an odd number...
list the scores in order (lowest to highest) and the median is the middle score on the list.
to find the median when n is an even number...
list the scores in order (lowest to highest) and then locate the median by finding the average of the middle two scores
step 2 t stat
locate critical region with df (consult table)
aspects of the experimental method
manipulation and control
the experimental method
manipulation and control to determine a cause/effect relationship, show that changing the value of one variable changes the value of another
changing the value of any score will change the
mean
every score in the distribution contributes to the value of the
mean
estimated d formula
mean difference/sample standard deviation
cohen's d formua
mean difference/standard deviation
μ
mean of a population
M
mean of a sample
z-scores make raw scores more _______
meaningful (Provide the location of the original X value within the distribution)
in a negatively skewed graph, from R to L you'll find the
mode, median, and then the mean
in a positively skewed graph, from L to R you'll find the...
mode, median, and then the mean
multiplying each score by a constant causes the standard deviation to be
multiplied by the same constant
A random sample is obtained from a population with μ = 80 and σ = 10. Which of the following samples would have the largest z-score?
n = 100 with M = 84
Which of the following would produce a standard error of 2 points?
n = 25 scores from a population with σ = 10
the greater the ____, better the distribution approximates normal
n, df
degrees of freedom formula
n-1
A sample obtained from a population with σ = 10 has a standard error of 2 points. The sample size is ____.
n=25
when does the distribution of sample means for sample size n reach normal
n=30
Which of the following deviation scores corresponds to the score that is farthest away from the mean?
negative ten (-10)
Using z-scores, a population with μ = 37 and σ = 6 is standardized so that the new mean is μ = 50 and σ = 10. How does an individual's z-score in the new distribution compare with his/her z-score in the original population?
new z = old z
why use median with open-ended distributions
no upper limit or lower limit for one of the categories, Impossible to compute a mean for these data, no ΣX
A sample of n = 4 scores has SS = 12. What is the standard deviation for the sample?
the square root of 4
If a distribution of scores is shown in a bar graph, you know that the scores were measured on a ___ scale of measurement.
nominal or ordinal
when to use the mode
nominal scales, discrete variables, describing shape
the shape of a sampling distribution is more or less...
normal
Which of the following is an example of a discrete variable? height, reaction time, number of brothers and/or sisters, age
number of brothers/sisters
N
number of scores in a population
n
number of scores in a sample
z-score distribution has a standard deviation of
one (1)
For the following scores, what is (∑ X) 2? Scores: 0, 1, 6, 3
one hundred 100
A population of N = 10 scores has a mean of μ = 24 with SS = 160, a variance of σ 2 = 16, and a standard deviation of σ = 4. For this population, ∑( X − μ) 2 has a value of ____.
one hundred and sixty (160)
A sample of n = 9 scores has SS = 72. What is the estimated standard error for the sample mean?
only 1
statistics help to bring ____ out of ______
order, chaos
After measuring two individuals, a researcher can say that Tom's score is greater than Bill's, but cannot specify how much greater. The measurements must come from a(n) ____ scale.
ordinal
y axis
ordinate
probability is expressed as
p(outcome)
A researcher is curious about the average IQ of registered voters in the state of Florida. If this average could be obtained, it would be an example of a sample/statistic/population/parameter ?
parameter
where is SUM ALL in the order of operations
parentheses, exponents, multiplication, division, sum all, addition, subraction (PEMDEAS)
r^2 is the
percentage of variance explained
Although research questions usually concern a ____, the actual research is typically conducted with a ____. sample, statistic/population, parameter / sample, population/population, sample
population, sample
What is the shape of the distribution for the following set of data? Scores: 1, 2, 2, 2, 2, 3, 3, 4, 5, 6
positively skewed
What shape would you expect for the distribution of scores from a very hard exam for a large class of students?
positively skewed
techniques to control other variables
random assignment, matching, holding them constant
After measuring a set of individuals, a researcher finds that Bob's score is three times greater than Jane's score. These measurements must come from a(n) ____ scale.
ratio
By selecting a smaller alpha level, a researcher is ___.
reducing the risk of a Type I error
sample standard deviation symbol
s
sample standard deviation
s = sqrt(s^2) = sqrt(SS/(n-1))
SM =
s/sqrt(n)
sample variance symbol
s^2
sample variance
s^2 = SS/(n-1) = SS/(number of scores free to vary = SS/df
the greater the value of df for a sample, the better ___ represents ____
s^2, σ^2
the standard error of M specifies how well a ___ estimates a _____
sample mean, population mean
what are the 2 factors that determine the magnitude of standard error
sample size, population standard deviation
s
sample standard deviation
SS/(n-1) is
sample variance
s^2
sample variance
s^2 is
sample variance
research uses ____ data to generalize about ____
sample, population
probability establishes a connection between....
samples and populations
a standardized distribution is composed of
scores that have been transformed to create predetermined values for μ and σ
Y
second variable
what does "setting the criteria" in a hypothesis test entail
setting an alpha level, thus defining the boundaries for the critical region
purpose of descriptive statistics
simplify data
Xmin
smallest score
in bimodal distributions, the mean and the median...
split the two modes
sample standard deviation
sqrt(SS/df)
sample standard deviation
sqrt(SS/n-1)
SM =
sqrt(s^2/n)
standard deviation in terms of variance
square root(variance)
the standard error of M measures the....
standard amount of difference between a sample mean (M) and the population mean (μ)
σ/sqrt(n) = sqrt(σ^2/n)
standard error
σM
standard error of M, standard distance between M and μ
z-scores _____ an entire distribution
standardize
steps of the t stat
state hypothesis & select alpha level, locate critial region w df, caclulate the t score, compare t score to critical region
step 1 t stat
state hypothesis and select alpha level
4 steps of hypothesis study
state the hypothesis, set the criteria for the decision, collect the data and compute sample statistics, make a decision
A researcher is interested in the effect of St. John's Wort on memory. A group of 25 college students are selected to participate in a research study. The average memory score obtained for the 25 students is a ____.
statistic
Standard error of M
the standard deviation of the distribution of sample means
the values in the distribution of sample means are not scores, but
statistics (sample means)
As sample size increases, the expected value of M ____.
stays constant
What is the first step to be performed when computing ∑( X-2) 2?
subtract 2 points from each score
SS
sum of squares
What is the final step to be performed in the following mathematical expression?∑( X + 2) 2
sum the squared values
E
summation
With α = .01, the two-tailed critical region for a sample of n = 20 subjects would have boundaries of ____.
t = ±2.861
the greater the value of df for a sample, the better the ___ approximates the _____
t statistic, z-score
r^2 =
t^2/(t^2+df)
holding them constant
technique to control other variables, Everyone the same age, etc.
matching
technique to control other variables, Match participant IQ's, etc
random assignment
technique to control other variables, Participant has equal chance of being assigned to each treatment Condition, Makes neither group smarter, stronger, faster, etc.
random sample requires that...
that each individual in the population has an equal chance of being selected, Probabilities must stay constant from one selection to the next if more than one individual is selected
Distribution of Sample Means
the collection of sample means for all possible random samples of a particular size (n) that can be obtained from a population
a scale of measurment is made up of
the complete set of categories
As sample size increases ____.
the critical values of t become smaller, the t distribution becomes more like a normal distribution, the value of df also increases
The mean of the distribution of sample means is called ____.
the expected value of M
Expected Value of M
the mean of the distribution of sample means is equal to μ
if every score in the distriubtion is multiplied/divided by a constant value
the mean will change in the same way
datum, score, or raw score
the measurement obtained for each individual
A researcher is measuring problem-solving times for a sample of n = 20 children. However, one of the children fails to solve the problem, so the researcher has an undetermined score. What is the best measure of central tendency for these data?
the median
sampling error
the natural discrepancy, or amount of error, between a sample statistic and its corresponding population parameter
dependent variable
the observed variable
in a t stat, the null hypothesis provides a specific value for
the population mean
the larger the sample size, the close the sample means should be to...
the population mean
if a constant value is added to/subtracted from every score in the distriubtion...
the same constant will be added to/subtracted from the mean
all intervals in a grouped frequency distribution should be...
the same width
A sample has a mean of M = 72. If one person with a score of X = 58 is removed from the sample, what effect will it have on the sample mean?
the sample mean will increase
Two samples from the same population both have n = 10 scores with M = 45. If the t statistic is computed for each sample, then ____.
the sample with the smaller variance will produce the larger t statistic
z-scores establish a relationship between what 3 things
the score, the mean, the standard deviation
minor mode
the smaller mode
The standard deviation of the distribution of sample means is called ____.
the standard error of M
The value for the range is determined by ____.
the two extreme scores (highest and lowest) in the distribution
purpose of central tendency
to find the single score that is most typical/representative of the entire group, Identify the "average" or "typical" individual , Makes large amounts of data more digestible
purpose of z scores (standard scores)
to identify and describe the exact location of every score in a distribution
purpose of frequency distribution
to obtain a relatively simple, organized picture of the data
purpose of variability
to obtain an objective measure of how the scores are spread out, describes the distribution (Tells whether scores are spread out/clustered, Defined in terms of distance), Measures how well an individual score (or group of scores) represents the entire distribution, Provides information on how much error to expect in using a sample to represent a population
A deviation of zero corresponds to a score exactly equal to the mean. t/f
true.
A jar contains 10 red marbles and 20 blue marbles. If you take a random sampling of two marbles from this jar, then the probability that the second marble is blue does not depend on the color of the first marble. t/f
true.
A population of N = 5 scores has SS = 20. The variance for this population is 4. t/f
true.
A professor records the height (in inches) for each student in a class. If these data are presented in a frequency distribution graph, it would be acceptable to use a polygon. t/f
true.
A researcher obtained M = 27 for a sample of n = 36 scores selected from a population with μ = 30 and σ = 12. This sample mean corresponds to a z-score of z = -1.50. t/f
true.
A researcher records how much time each participant needs to solve a series of problems. This is an example of a continuous variable. t/f
true.
A researcher records the gender of each child born in the county hospital during the month of June. This researcher is measuring a discrete variable. t/f
true.
After the scores in a sample have been organized into a frequency distribution table, you can determine the number of scores (n) by simply adding the values in the f column of the table. t/f
true.
Assuming that all other factors are held constant, as the population variability increases, the standard error will also increase. t/f
true.
For a normal distribution, the proportion in the tail beyond z = +1.00 is exactly the same as the proportion in the tail beyond z = -1.00. t/f
true.
For a specific set of scores, the value you obtain for SS will be the same whether the set of scores is a sample or a population. t/f
true.
For any normal distribution, exactly 2.5% of the scores are located in the tail beyond z = 1.96. t/f
true.
For any population, a z-score of +1.00 corresponds to a location above the mean by one standard deviation. t/f
true.
For the following scores, (∑ X) 2 = 100. Scores: 1, 2, 3, 4 t/f
true.
If a deviation score has a negative (−) sign, then the X value is below the mean. t/f
true.
If a distribution of scores is transformed into z-scores then the sum of the positive z-scores will be exactly equal to the sum of the negative z-scores. t/f
true.
If other factors are held constant, then increasing the sample size will increase the likelihood of rejecting the null hypothesis. t/f
true.
If two individuals in a population have identical X scores, they also will have identical z-scores. t/f
true.
In a research report, the term statistically significant is used to indicate that the null hypothesis was rejected. t/f
true.
In general, an increase in the sample size makes it more likely that the t statistic will be large enough to reject the null hypothesis.
true.
In general, the null hypothesis states that the treatment has no effect on the population mean. t/f
true.
In the text, the definition of a random sample requires sampling with replacement. t/f
true.
It is possible for the distribution of sample means to be normal even if it is based on samples with less than n = 30. t/f
true.
It is possible to have a distribution of scores where no individual has a score exactly equal to the mean. t/f
true.
Measures of effect size, such as r2 or Cohen's d, are not greatly influenced by sample size. t/f
true.
Measuring the number of students in each psychology course would be an example of a discrete variable. t/f
true.
No single method will provide a good measure of central tendency for every possible set of data. t/f
true.
On an exam with μ = 70, you have a score of X = 76. You should expect a better grade if σ = 3 than if σ = 12. t/f
true.
One purpose for central tendency is to describe an entire distribution by identifying the most representative score. t/f
true.
The normal-shaped distribution is an example of a symmetrical distribution. t/f
true.
The standard error for a sample mean can never be larger than the standard deviation of the population from which the sample is selected. t/f
true.
The t statistic is used for hypothesis tests in situations where the population standard deviation (or variance) is unknown. t/f
true.
To determine how much difference there is between two individuals, you must use either an interval or a ratio scale of measurement. t/f
true.
Transforming an entire distribution of scores into z-scores will not change the shape of the distribution. t/f
true.
Two samples probably will have different means even if they are both the same size and they are both selected from the same population. t/f
true.
When calculating SS, it is impossible to obtain a value less than zero unless a mistake is made. t/f
true.
A population of scores has μ = 80. In this population, a score of X = 86 corresponds to z = +3. What is the population standard deviation?
two (2)
bimodal
two modes, Often an indication that two separate and distinct groups exist within the same sample
y axis should ____ length of axis
two thirds
multimodal
two+ modes
adding a constant to each score will _____ the standard deviation
unaffect
the sample mean is an example of an ____ statistic
unbiased
X
unchanged, original raw scores
hypothesis tests with the t stat begin with a population with a ___ mean and ____ variance
unknown, unknown
t statistic
used to test hypotheses about an unknown population mean μ when the value of σ is unknown
problem with z-scores
usually require more information than available (population standard deviation/variance)
2 basic assumptions of t score formula
values in sample must consist of indepdent observations (no pattern), population must be normal
probability can be used to predict...
what kind of samples are likely to be obtained from a population
when is a sample statistic unbiased
when the average value of the sample statistic, obtained over many different samples, is equal to the population parameter.
Under what circumstances would a score that is located 5 points above the mean be considered relatively close to the mean?
when the population standard deviation is much greater than 5
Under what circumstances would a score that is 15 points above the mean be considered an extreme score?
when the population standard deviation is much smaller than 15
in a z score, +/- sign tells...
whether score is above or below the mean
if Xmin is 45, the LRL is
would be 44.5
if Xmax is 45, the URL is
would be 45.5
do an x value graph and z-score graph have the same shape
yes
do the number of scores in a sample affect the t stat
yes
does the magnitude of sample variance have an effect on t stat
yes
For a distribution of scores, which of the following z-score values represents the location closest to the mean?
z = +0.50
In a normal distribution, what z-score value separates the lowest 20% of the distribution from the highest 80%?
z = -0.84
For a distribution of scores, which of the following z-score values represents the most extreme location on the left-hand side of the distribution?
z = -2.00
z-score for samples
z=(X-M)/s
A random sample of n = 9 scores is obtained from a population with μ = 50 and σ = 9. If the sample mean is M = 59, what is the z-score corresponding to the sample mean?
z=3.00
What is the variance for the following population of scores? Scores: 2, 2, 2, 2
zero
A sample of n = 20 scores is transformed into z-scores. The mean for the 20 z-scores is ____.
zero (0)
The mean for any distribution corresponds to a z-score of ____.
zero (0)
z-score distribution mean
zero (0)
For a normal distribution, the proportion in the tail beyond z = 1.50 is p = 0.0668. Based on this information, what is the proportion in the tail beyond z = −1.50?
zero point zero six six 8 (0.0668)
μ =
ΣX/N
M =
ΣX/n
The symbol that corresponds to the expected value of M is ____.
μ
A population of scores has μ = 20 and σ = 5. If two points are added to every score in the population, then the new values for the mean and standard deviation would be ____.
μ = 22 and σ = 5
A population of scores has μ = 20 and σ = 5. If every score in the population is multiplied by 2, then the new values for the mean and standard deviation would be ____.
μ = 40 and σ = 10
In a population with σ = 8, a score of X = 42 corresponds to a z-score of z = −0.50. What is the population mean?
μ = 46
Suppose you earned a score of X = 54 on an exam. Which set of parameters would give you the highest grade?
μ = 50 and σ = 2
If you have a score of X = 75 on an exam, which set of parameters would give you the highest position within the class?
μ = 60 and σ = 5
A researcher is conducting an experiment to evaluate a treatment that is expected to increase the scores for individuals in a population that is known to have a mean of μ = 80. The results will be examined using a one-tailed hypothesis test. Which of the following is the correct statement of the null hypothesis?
μ ≤ 80
A population with μ = 85 and σ = 12 is transformed into z-scores. After the transformation, the population of z-scores will have a standard deviation of ____.
σ = 1.00
On an exam with a mean of μ = 70, you have a score of X = 65. Which of the following values for the standard deviation would give you the highest position within the class?
σ = 10
A researcher uses a hypothesis test to evaluate H 0 μ = 80. If the researcher obtains a sample mean of M = 88, which combination of factors is most likely to result in rejecting the null hypothesis?
σ = 5 and n = 50
A researcher uses a hypothesis test to evaluate H 0 μ = 80. If the researcher obtains a sample mean of M = 88, which combination of factors is most likely to result in rejecting the null hypothesis?
σ = 5 and α = .05
The symbol that corresponds to the standard error of M is ____.
σ M
σM =
σ/√n = √(σ^2/n)
standard error
σM = σ/sqrt(n) = sqrt(σ^2/n)
How would the following mathematical operation be expressed in summation notation? "Add two points to each score, square the resulting value, then find the sum of the squared numbers."
∑( X + 2) 2
