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Test your basic knowledge |
CLEP General Mathematics: Probability And Statistics
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clep
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Instructions:
Answer 50 questions in 15 minutes.
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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. A sample selected in such a way that each individual is equally likely to be selected as well as any group of size n is equally likely to be selected.
Independent Selection
Probability and statistics
Simple random sample
Confounded variables
2. A variable describes an individual by placing the individual into a category or a group.
Descriptive statistics
the population cumulants
Type II errors
Qualitative variable
3. Probability of rejecting a true null hypothesis.
P-value
Seasonal effect
Alpha value (Level of Significance)
Independent Selection
4. Some commonly used symbols for population parameters
The Expected value
the population mean
A probability distribution
Type I errors
5. The probability distribution of a sample statistic based on all the possible simple random samples of the same size from a population.
Sampling Distribution
An experimental study
Individual
descriptive statistics
6. To find the average - or arithmetic mean - of a set of numbers:
Experimental and observational studies
Type I errors
Divide the sum by the number of values.
Power of a test
7. Given two jointly distributed random variables X and Y - the conditional probability distribution of Y given X (written 'Y | X') is the probability distribution of Y when X is known to be a particular value.
Conditional distribution
Simulation
A Random vector
Marginal probability
8. Because variables conforming only to nominal or ordinal measurements cannot be reasonably measured numerically - sometimes they are grouped together as
Type II errors
The variance of a random variable
A statistic
categorical variables
9. In number theory - scatter plots of data generated by a distribution function may be transformed with familiar tools used in statistics to reveal underlying patterns - which may then lead to
hypotheses
An experimental study
Kurtosis
Confounded variables
10. A numerical measure that describes an aspect of a sample.
Statistic
hypothesis
Independent Selection
Step 3 of a statistical experiment
11. 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
Variability
variance of X
Probability
Law of Large Numbers
12. Probability of accepting a false null hypothesis.
Ordinal measurements
The variance of a random variable
Alpha value (Level of Significance)
Beta value
13. Involves taking measurements of the system under study - manipulating the system - and then taking additional measurements using the same procedure to determine if the manipulation has modified the values of the measurements.
Independence or Statistical independence
Descriptive
Conditional distribution
An experimental study
14. E[X] :
Type II errors
The sample space
Variability
expected value of X
15. (or just likelihood) is a conditional probability function considered a function of its second argument with its first argument held fixed. For example - imagine pulling a numbered ball with the number k from a bag of n balls - numbered 1 to n. Then
Bias
Descriptive
applied statistics
A likelihood function
16. Is a sample and the associated data points.
A data set
the population mean
An estimate of a parameter
Quantitative variable
17. The standard deviation of a sampling distribution.
Lurking variable
Standard error
Simulation
Parameter - or 'statistical parameter'
18. Also called correlation coefficient - is a numeric measure of the strength of linear relationship between two random variables (one can use it to quantify - for example - how shoe size and height are correlated in the population). An example is the P
Divide the sum by the number of values.
Skewness
Correlation
Marginal distribution
19. There are four main levels of measurement used in statistics: Each of these have different degrees of usefulness in statistical research.
A likelihood function
nominal - ordinal - interval - and ratio
A Statistical parameter
Prior probability
20. Is data arising from counting that can take only non-negative integer values.
A sample
Variability
A probability space
Count data
21. Are two related but separate academic disciplines. Statistical analysis often uses probability distributions - and the two topics are often studied together. However - probability theory contains much that is of mostly of mathematical interest and no
Kurtosis
Law of Parsimony
Dependent Selection
Probability and statistics
22. Can be a population parameter - a distribution parameter - an unobserved parameter (with different shades of meaning). In statistics - this is often a quantity to be estimated.
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23. Given two jointly distributed random variables X and Y - the marginal distribution of X is simply the probability distribution of X ignoring information about Y.
Marginal distribution
The Range
expected value of X
Ordinal measurements
24. Are simply two different terms for the same thing. Add the given values
Probability
Average and arithmetic mean
A population or statistical population
Quantitative variable
25. Is a typed measurement - it can be a boolean value - a real number - a vector (in which case it's also called a data vector) - etc.
A data point
Descriptive statistics
inferential statistics
the sample or population mean
26. Is the probability distribution - under repeated sampling of the population - of a given statistic.
A sampling distribution
The Covariance between two random variables X and Y - with expected values E(X) =
An event
Statistical dispersion
27. Another name for elementary event.
Step 1 of a statistical experiment
Experimental and observational studies
Marginal probability
Atomic event
28. Is a sample space over which a probability measure has been defined.
Ratio measurements
A probability space
the population correlation
A Distribution function
29. Statistics involve methods of using information from a sample to draw conclusions regarding the population.
Independence or Statistical independence
The sample space
Null hypothesis
Inferential
30. Any specific experimental condition applied to the subjects
Treatment
the population correlation
Type I errors
quantitative variables
31. 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
Probability
Independence or Statistical independence
Simulation
Individual
32. Is inference about a population from a random sample drawn from it or - more generally - about a random process from its observed behavior during a finite period of time.
Correlation coefficient
Statistical inference
Qualitative variable
Type I errors
33. There are two major types of causal statistical studies: In both types of studies - the effect of differences of an independent variable (or variables) on the behavior of the dependent variable are observed. The difference between the two types lies
Sample space
experimental studies and observational studies.
The standard deviation
Parameter - or 'statistical parameter'
34. Is a parameter that indexes a family of probability distributions.
Marginal probability
Random variables
Correlation
A Statistical parameter
35. ?r
The Expected value
Statistics
the population cumulants
The standard deviation
36. Is defined as the expected value of random variable (X -
Greek letters
The Covariance between two random variables X and Y - with expected values E(X) =
Type I errors & Type II errors
The sample space
37. A numerical facsimilie or representation of a real-world phenomenon.
That is the median value
Reliable measure
Simulation
f(z) - and its cdf by F(z).
38. Two variables such that their effects on the response variable cannot be distinguished from each other.
An experimental study
Confounded variables
Probability and statistics
Prior probability
39. Error also refers to the extent to which individual observations in a sample differ from a central value - such as
Correlation coefficient
Quantitative variable
covariance of X and Y
the sample or population mean
40. When there is an even number of values...
Standard error
Conditional distribution
That is the median value
Placebo effect
41. In the long run - as the sample size increases - the relative frequencies of outcomes approach to the theoretical probability.
the sample or population mean
Law of Large Numbers
An Elementary event
Sampling Distribution
42. In particular - the pdf of the standard normal distribution is denoted by
The standard deviation
observational study
f(z) - and its cdf by F(z).
Valid measure
43. A common goal for a statistical research project is to investigate causality - and in particular to draw a conclusion on the effect of changes in the values of predictors or independent variables on dependent variables or response.
Count data
Posterior probability
Experimental and observational studies
Correlation
44. Long-term upward or downward movement over time.
the sample or population mean
Trend
Step 1 of a statistical experiment
A probability space
45. 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
Statistical adjustment
Statistical dispersion
Descriptive statistics
Lurking variable
46. The probability of the observed value or something more extreme under the assumption that the null hypothesis is true.
P-value
Count data
Interval measurements
Standard error
47. (e.g. ? - b) are commonly used to denote unknown parameters (population parameters).
Divide the sum by the number of values.
categorical variables
Greek letters
The median value
48. Is a function that gives the probability of all elements in a given space: see List of probability distributions
Statistical dispersion
A probability distribution
The sample space
quantitative variables
49. A measure that is relevant or appropriate as a representation of that property.
The sample space
An estimate of a parameter
Independence or Statistical independence
Valid measure
50. Is the set of possible outcomes of an experiment. For example - the sample space for rolling a six-sided die will be {1 - 2 - 3 - 4 - 5 - 6}.
The sample space
Valid measure
Sampling
the population variance