Stats Midterm ALL

¡Supera tus tareas y exámenes ahora con Quizwiz!

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


Conjuntos de estudio relacionados

MUSIC-15: Music Business Final Review

View Set

Supply Chain Design & Management Exams

View Set

Certify Teacher Study Mode PPR (EC-12) - Domain 2: CREATING A POSITIVE, PRODUCTIVE CLASSROOM ENVIRONMENT

View Set

Chapter 17.5 - Managing Organizational Communication

View Set

Chapter 52: Care of the Patient with a Sensory Disorder

View Set