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Test your basic knowledge |
CLEP General Mathematics: Probability And Statistics
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clep
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math
Instructions:
Answer 50 questions in 15 minutes.
If you are not ready to take this test, you can
study here
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Match each statement with the correct term.
Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.
This is a study tool. The 3 wrong answers for each question are randomly chosen from answers to other questions. So, you might find at times the answers obvious, but you will see it re-enforces your understanding as you take the test each time.
1. Occurs when a subject receives no treatment - but (incorrectly) believes he or she is in fact receiving treatment and responds favorably.
methods of least squares
Placebo effect
Sampling frame
Independent Selection
2. Is the study of the collection - organization - analysis - and interpretation of data. It deals with all aspects of this - including the planning of data collection in terms of the design of surveys and experiments.
the population mean
Statistics
The variance of a random variable
A likelihood function
3. Because variables conforming only to nominal or ordinal measurements cannot be reasonably measured numerically - sometimes they are grouped together as
categorical variables
Bias
Posterior probability
Statistic
4. (also called statistical variability) is a measure of how diverse some data is. It can be expressed by the variance or the standard deviation.
Statistical dispersion
Dependent Selection
Quantitative variable
Lurking variable
5. Failing to reject a false null hypothesis.
Power of a test
Statistic
Type 2 Error
Count data
6. Have imprecise differences between consecutive values - but have a meaningful order to those values
Step 3 of a statistical experiment
Treatment
Ordinal measurements
A probability distribution
7. Is the probability of an event - ignoring any information about other events. The marginal probability of A is written P(A). Contrast with conditional probability.
An estimate of a parameter
Marginal probability
Greek letters
Independent Selection
8. Is a measure of the asymmetry of the probability distribution of a real-valued random variable. Roughly speaking - a distribution has positive skew (right-skewed) if the higher tail is longer and negative skew (left-skewed) if the lower tail is longe
The median value
A random variable
Particular realizations of a random variable
Skewness
9. Where the null hypothesis fails to be rejected and an actual difference between populations is missed giving a 'false negative'.
Alpha value (Level of Significance)
Marginal probability
Type II errors
Joint distribution
10. S^2
the population variance
Binary data
Random variables
Probability density
11. Is a set of entities about which statistical inferences are to be drawn - often based on random sampling. One can also talk about a population of measurements or values.
A population or statistical population
A statistic
covariance of X and Y
Atomic event
12. A scale that represents an ordinal scale such as looks on a scale from 1 to 10.
Likert scale
Bias
quantitative variables
experimental studies and observational studies.
13. Uses patterns in the sample data to draw inferences about the population represented - accounting for randomness. These inferences may take the form of: answering yes/no questions about the data (hypothesis testing) - estimating numerical characteris
the population variance
Seasonal effect
Conditional distribution
Inferential statistics
14. In particular - the pdf of the standard normal distribution is denoted by
P-value
Ratio measurements
f(z) - and its cdf by F(z).
applied statistics
15. Working from a null hypothesis two basic forms of error are recognized:
hypothesis
Statistics
Type 1 Error
Type I errors & Type II errors
16. The standard deviation of a sampling distribution.
That is the median value
Sampling frame
Standard error
Law of Parsimony
17. Patterns in the data may be modeled in a way that accounts for randomness and uncertainty in the observations - and are then used for drawing inferences about the process or population being studied; this is called
A random variable
inferential statistics
A data set
Alpha value (Level of Significance)
18. A variable that has an important effect on the response variable and the relationship among the variables in a study but is not one of the explanatory variables studied either because it is unknown or not measured.
An event
Lurking variable
A statistic
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
19. The probability distribution of a sample statistic based on all the possible simple random samples of the same size from a population.
Sampling Distribution
Coefficient of determination
the population mean
Bias
20. ?
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
the population correlation
Joint distribution
Binary data
21. Is a function that gives the probability of all elements in a given space: see List of probability distributions
Dependent Selection
The Expected value
Pairwise independence
A probability distribution
22. Two events are independent if the outcome of one does not affect that of the other (for example - getting a 1 on one die roll does not affect the probability of getting a 1 on a second roll). Similarly - when we assert that two random variables are i
Independence or Statistical independence
Treatment
Simpson's Paradox
An experimental study
23. Have meaningful distances between measurements defined - but the zero value is arbitrary (as in the case with longitude and temperature measurements in Celsius or Fahrenheit)
A sampling distribution
Interval measurements
The Mean of a random variable
Sampling
24. Is the function that gives the probability distribution of a random variable. It cannot be negative - and its integral on the probability space is equal to 1.
Interval measurements
Parameter - or 'statistical parameter'
A Distribution function
Step 2 of a statistical experiment
25. There are four main levels of measurement used in statistics: Each of these have different degrees of usefulness in statistical research.
Skewness
nominal - ordinal - interval - and ratio
Type I errors & Type II errors
Beta value
26. Is the length of the smallest interval which contains all the data.
Law of Large Numbers
A likelihood function
observational study
The Range
27. Ratio and interval measurements which can be either discrete or continuous - due to their numerical nature are grouped together as
the population variance
Parameter - or 'statistical parameter'
quantitative variables
Statistical adjustment
28. Long-term upward or downward movement over time.
Divide the sum by the number of values.
Sample space
Variable
Trend
29. Descriptive statistics and inferential statistics (a.k.a. - predictive statistics) together comprise
Simulation
applied statistics
the sample or population mean
An experimental study
30. Statistical methods can be used for summarizing or describing a collection of data; this is called
descriptive statistics
hypotheses
That is the median value
Ordinal measurements
31. A consistent - repeated deviation of the sample statistic from the population parameter in the same direction when many samples are taken.
s-algebras
Bias
quantitative variables
Variable
32. Gives the probability of events in a probability space.
Statistical adjustment
A Probability measure
Bias
categorical variables
33. Rejecting a true null hypothesis.
Type 1 Error
Qualitative variable
Type I errors
Dependent Selection
34. Samples are drawn from two different populations such that the sample data drawn from one population is completely unrelated to the selection of sample data from the other population.
Skewness
inferential statistics
Law of Large Numbers
Independent Selection
35. Is data arising from counting that can take only non-negative integer values.
A Random vector
Count data
Descriptive
Statistical dispersion
36. Are written in corresponding lower case letters. For example x1 - x2 - ... - xn could be a sample corresponding to the random variable X.
Statistics
A probability density function
A Probability measure
Particular realizations of a random variable
37. (or atomic event) is an event with only one element. For example - when pulling a card out of a deck - 'getting the jack of spades' is an elementary event - while 'getting a king or an ace' is not.
Conditional distribution
Seasonal effect
An Elementary event
The sample space
38. Is a measure of the 'peakedness' of the probability distribution of a real-valued random variable. Higher kurtosis means more of the variance is due to infrequent extreme deviations - as opposed to frequent modestly sized deviations.
Simpson's Paradox
Interval measurements
Kurtosis
Sampling frame
39. The objects described by a set of data: person (animal) - place - and - thing. (SUBJECTS)
Individual
The average - or arithmetic mean
hypothesis
Statistical inference
40. Is often denoted by placing a caret over the corresponding symbol - e.g. - pronounced 'theta hat'.
Ratio measurements
An estimate of a parameter
Type II errors
f(z) - and its cdf by F(z).
41. A numerical measure that describes an aspect of a sample.
the population correlation
Type I errors
Statistic
hypotheses
42. Is used to describe probability in a continuous probability distribution. For example - you can't say that the probability of a man being six feet tall is 20% - but you can say he has 20% of chances of being between five and six feet tall. Probabilit
A probability density function
That value is the median value
Probability density
methods of least squares
43. The probability of correctly detecting a false null hypothesis.
Reliable measure
Power of a test
Likert scale
Conditional probability
44. Error also refers to the extent to which individual observations in a sample differ from a central value - such as
the sample or population mean
Inferential statistics
Skewness
Block
45. When there is an even number of values...
Skewness
Sample space
That is the median value
the population variance
46. Any specific experimental condition applied to the subjects
quantitative variables
Treatment
The Covariance between two random variables X and Y - with expected values E(X) =
Type I errors
47. Is one that explores the correlation between smoking and lung cancer. This type of study typically uses a survey to collect observations about the area of interest and then performs statistical analysis. In this case - the researchers would collect o
Step 2 of a statistical experiment
Law of Parsimony
Correlation coefficient
Observational study
48. Summarize the population data by describing what was observed in the sample numerically or graphically. Numerical descriptors include mean and standard deviation for continuous data types (like heights or weights) - while frequency and percentage are
Descriptive statistics
Bias
Sampling Distribution
Observational study
49. Is used in 'mathematical statistics' (alternatively - 'statistical theory') to study the sampling distributions of sample statistics and - more generally - the properties of statistical procedures. The use of any statistical method is valid when the
Type I errors & Type II errors
Kurtosis
Placebo effect
Probability
50. A numerical measure that describes an aspect of a population.
descriptive statistics
Kurtosis
Lurking variable
Parameter