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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.
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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.
Simple random sample
Random variables
A Random vector
variance of X
2. 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
Correlation coefficient
Observational study
Parameter - or 'statistical parameter'
Qualitative variable
3. Any specific experimental condition applied to the subjects
Quantitative variable
Beta value
Joint distribution
Treatment
4. Performing the experiment following the experimental protocol and analyzing the data following the experimental protocol. 4. Further examining the data set in secondary analyses - to suggest new hypotheses for future study. 5. Documenting and present
Simulation
Step 3 of a statistical experiment
Qualitative variable
experimental studies and observational studies.
5. 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
Inferential statistics
A population or statistical population
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
the population correlation
6. Are written in corresponding lower case letters. For example x1 - x2 - ... - xn could be a sample corresponding to the random variable X.
Sampling frame
Marginal distribution
Particular realizations of a random variable
Pairwise independence
7. 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
The median value
A probability density function
Variable
Independence or Statistical independence
8. 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.
Type 1 Error
methods of least squares
Probability and statistics
Statistical inference
9. There are four main levels of measurement used in statistics: Each of these have different degrees of usefulness in statistical research.
nominal - ordinal - interval - and ratio
Marginal distribution
Variable
Cumulative distribution functions
10. (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.
Law of Large Numbers
An Elementary event
hypotheses
Sampling
11. Where the null hypothesis is falsely rejected giving a 'false positive'.
Atomic event
Type I errors
Type I errors & Type II errors
Joint probability
12. 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
Trend
Probability and statistics
An Elementary event
Coefficient of determination
13. Var[X] :
Treatment
observational study
variance of X
Independent Selection
14. The probability distribution of a sample statistic based on all the possible simple random samples of the same size from a population.
Conditional distribution
Simulation
The Covariance between two random variables X and Y - with expected values E(X) =
Sampling Distribution
15. 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.
Marginal probability
Kurtosis
A probability density function
Quantitative variable
16. Is the probability of some event A - assuming event B. Conditional probability is written P(A|B) - and is read 'the probability of A - given B'
The Covariance between two random variables X and Y - with expected values E(X) =
Trend
Conditional probability
Null hypothesis
17. 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.
Conditional probability
Kurtosis
Null hypothesis
Statistical adjustment
18. The collection of all possible outcomes in an experiment.
Sample space
Posterior probability
nominal - ordinal - interval - and ratio
Null hypothesis
19. Data are gathered and correlations between predictors and response are investigated.
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Count data
observational study
The Range
20. Is the result of applying a statistical algorithm to a data set. It can also be described as an observable random variable.
Quantitative variable
Marginal distribution
Coefficient of determination
A statistic
21. 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
hypotheses
Posterior probability
Probability
Treatment
22. Samples are drawn from two different populations such that there is a matching of the first sample data drawn and a corresponding data value in the second sample data.
Independence or Statistical independence
Atomic event
Sample space
Dependent Selection
23. 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
Skewness
Marginal distribution
Sampling frame
Posterior probability
24. A collection of events is mutually independent if for any subset of the collection - the joint probability of all events occurring is equal to the product of the joint probabilities of the individual events. Think of the result of a series of coin-fl
Joint distribution
Mutual independence
A Random vector
Probability and statistics
25. Describes the spread in the values of the sample statistic when many samples are taken.
Marginal probability
hypotheses
Variability
Independence or Statistical independence
26. Another name for elementary event.
experimental studies and observational studies.
Beta value
Atomic event
Sampling
27. Is data that can take only two values - usually represented by 0 and 1.
A Random vector
Binary data
Marginal probability
the population mean
28. The proportion of the explained variation by a linear regression model in the total variation.
Step 2 of a statistical experiment
The median value
variance of X
Coefficient of determination
29. The probability of the observed value or something more extreme under the assumption that the null hypothesis is true.
Marginal probability
Type I errors & Type II errors
Nominal measurements
P-value
30. Have both a meaningful zero value and the distances between different measurements defined; they provide the greatest flexibility in statistical methods that can be used for analyzing the data
Law of Large Numbers
Atomic event
Particular realizations of a random variable
Ratio measurements
31. (pdfs) and probability mass functions are denoted by lower case letters - e.g. f(x).
A probability density function
Probability density functions
nominal - ordinal - interval - and ratio
Type I errors & Type II errors
32. Is a function of the known data that is used to estimate an unknown parameter; an estimate is the result from the actual application of the function to a particular set of data. The mean can be used as an estimator.
the population mean
Estimator
Joint probability
Quantitative variable
33. S^2
Particular realizations of a random variable
the population variance
variance of X
Simpson's Paradox
34. ?
Statistic
the population correlation
the population mean
Inferential statistics
35. A numerical measure that assesses the strength of a linear relationship between two variables.
Residuals
Conditional probability
Qualitative variable
Correlation coefficient
36. The standard deviation of a sampling distribution.
Standard error
Step 3 of a statistical experiment
Power of a test
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
37. Are usually written with upper case calligraphic (e.g. F for the set of sets on which we define the probability P)
The sample space
hypotheses
s-algebras
A probability space
38. 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
Conditional distribution
Interval measurements
the population cumulants
inferential statistics
39. Is a measure of its statistical dispersion - indicating how far from the expected value its values typically are. The variance of random variable X is typically designated as - - or simply s2.
A sampling distribution
The sample space
nominal - ordinal - interval - and ratio
The variance of a random variable
40. Some commonly used symbols for sample statistics
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
Placebo effect
Joint distribution
A population or statistical population
41. (cdfs) are denoted by upper case letters - e.g. F(x).
Cumulative distribution functions
Placebo effect
An estimate of a parameter
Binomial experiment
42. Probability of rejecting a true null hypothesis.
Bias
Alpha value (Level of Significance)
An estimate of a parameter
Probability density functions
43. Statistics involve methods of organizing - picturing - and summarizing information from samples or population.
Step 2 of a statistical experiment
Correlation coefficient
Descriptive
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
44.
Bias
Treatment
the population mean
Block
45. Interpretation of statistical information in that the assumption is that whatever is proposed as a cause has no effect on the variable being measured can often involve the development of a
the population variance
Correlation coefficient
Type I errors & Type II errors
Null hypothesis
46. In the long run - as the sample size increases - the relative frequencies of outcomes approach to the theoretical probability.
Sample space
Credence
Law of Large Numbers
inferential statistics
47. Ratio and interval measurements which can be either discrete or continuous - due to their numerical nature are grouped together as
categorical variables
quantitative variables
Placebo effect
Posterior probability
48. E[X] :
A data point
the population correlation
Type II errors
expected value of X
49. Probability of accepting a false null hypothesis.
The Covariance between two random variables X and Y - with expected values E(X) =
Variability
Probability density functions
Beta value
50. Can refer either to a sample not being representative of the population - or to the difference between the expected value of an estimator and the true value.
Variability
quantitative variables
Bias
Lurking variable