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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. Rejecting a true null hypothesis.
Qualitative variable
Coefficient of determination
Type 1 Error
Pairwise independence
2. Working from a null hypothesis two basic forms of error are recognized:
the population mean
Lurking variable
Residuals
Type I errors & Type II errors
3. 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.
covariance of X and Y
Statistical dispersion
Simple random sample
Cumulative distribution functions
4. 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
Lurking variable
Simpson's Paradox
observational study
Skewness
5. Consists of a number of independent trials repeated under identical conditions. On each trial - there are two possible outcomes.
variance of X
Residuals
An Elementary event
Binomial experiment
6. (pdfs) and probability mass functions are denoted by lower case letters - e.g. f(x).
Probability density functions
A Statistical parameter
A sampling distribution
the population cumulants
7. Planning the research - including finding the number of replicates of the study - using the following information: preliminary estimates regarding the size of treatment effects - alternative hypotheses - and the estimated experimental variability. Co
Descriptive statistics
Law of Parsimony
Step 1 of a statistical experiment
Conditional distribution
8. 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.
Type 2 Error
Kurtosis
Null hypothesis
A data set
9. A data value that falls outside the overall pattern of the graph.
hypothesis
the population cumulants
Outlier
observational study
10. Because variables conforming only to nominal or ordinal measurements cannot be reasonably measured numerically - sometimes they are grouped together as
Probability
categorical variables
Power of a test
A population or statistical population
11. The standard deviation of a sampling distribution.
Correlation coefficient
Standard error
applied statistics
Divide the sum by the number of values.
12. The probability of the observed value or something more extreme under the assumption that the null hypothesis is true.
P-value
The Mean of a random variable
Type 1 Error
Outlier
13. 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.
Simpson's Paradox
Reliable measure
categorical variables
A population or statistical population
14. (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.
Dependent Selection
descriptive statistics
f(z) - and its cdf by F(z).
An Elementary event
15. In particular - the pdf of the standard normal distribution is denoted by
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
observational study
the population cumulants
f(z) - and its cdf by F(z).
16. Is a subset of the sample space - to which a probability can be assigned. For example - on rolling a die - 'getting a five or a six' is an event (with a probability of one third if the die is fair).
An event
Block
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
Standard error
17. Is often denoted by placing a caret over the corresponding symbol - e.g. - pronounced 'theta hat'.
expected value of X
Probability density functions
methods of least squares
An estimate of a parameter
18. 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
Confounded variables
Sampling frame
Probability density
A data point
19. A scale that represents an ordinal scale such as looks on a scale from 1 to 10.
A random variable
Likert scale
Experimental and observational studies
Joint probability
20. (or expectation) of a random variable is the sum of the probability of each possible outcome of the experiment multiplied by its payoff ('value'). Thus - it represents the average amount one 'expects' to win per bet if bets with identical odds are re
The Expected value
Descriptive
variance of X
Step 2 of a statistical experiment
21. Statistics involve methods of organizing - picturing - and summarizing information from samples or population.
Descriptive
A Distribution function
The median value
Marginal probability
22. Another name for elementary event.
Atomic event
Variable
Residuals
quantitative variables
23. Is a function that gives the probability of all elements in a given space: see List of probability distributions
Null hypothesis
A probability distribution
Independence or Statistical independence
Residuals
24. Design of experiments - using blocking to reduce the influence of confounding variables - and randomized assignment of treatments to subjects to allow unbiased estimates of treatment effects and experimental error. At this stage - the experimenters a
Step 2 of a statistical experiment
Mutual independence
Correlation coefficient
The average - or arithmetic mean
25. 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
Average and arithmetic mean
Binary data
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
Null hypothesis
26. 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.
the population variance
Particular realizations of a random variable
An event
Independent Selection
27. 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.
Ordinal measurements
Experimental and observational studies
Treatment
Conditional probability
28. 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
Sampling
That is the median value
Sampling Distribution
experimental studies and observational studies.
29. Is a sample space over which a probability measure has been defined.
Kurtosis
A probability space
Parameter - or 'statistical parameter'
Confounded variables
30. 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.
31. 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
Independence or Statistical independence
Estimator
The Mean of a random variable
Descriptive statistics
32. 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
Statistical dispersion
Parameter - or 'statistical parameter'
Mutual independence
Sampling Distribution
33. 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
Skewness
A data point
Independence or Statistical independence
A probability distribution
34. Can be - for example - the possible outcomes of a dice roll (but it is not assigned a value). The distribution function of a random variable gives the probability of different results. We can also derive the mean and variance of a random variable.
Dependent Selection
Statistic
A random variable
Greek letters
35. Error also refers to the extent to which individual observations in a sample differ from a central value - such as
A sampling distribution
Estimator
the sample or population mean
Quantitative variable
36. 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.
Likert scale
The variance of a random variable
Experimental and observational studies
covariance of X and Y
37. 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.
the population mean
Seasonal effect
Statistic
Bias
38. A variable has a value or numerical measurement for which operations such as addition or averaging make sense.
Outlier
Quantitative variable
Probability
Correlation
39. Statistics involve methods of using information from a sample to draw conclusions regarding the population.
Sample space
Inferential
Bias
A likelihood function
40. (e.g. ? - b) are commonly used to denote unknown parameters (population parameters).
Conditional probability
Particular realizations of a random variable
Greek letters
Marginal probability
41. Are usually written in upper case roman letters: X - Y - etc.
That is the median value
An estimate of a parameter
Random variables
The variance of a random variable
42. Is the exact middle value of a set of numbers Arrange the numbers in numerical order. Find the value in the middle of the list.
Statistical dispersion
Atomic event
The median value
Block
43. To find the median value of a set of numbers: Arrange the numbers in numerical order. Locate the two middle numbers in the list. Find the average of those two middle values.
A probability distribution
Law of Parsimony
That value is the median value
Lurking variable
44. Gives the probability distribution for a continuous random variable.
Skewness
A probability density function
Step 1 of a statistical experiment
Alpha value (Level of Significance)
45. Var[X] :
The Range
Valid measure
Descriptive statistics
variance of X
46. Is a parameter that indexes a family of probability distributions.
A Statistical parameter
Placebo effect
A Probability measure
Interval measurements
47. In Bayesian inference - this represents prior beliefs or other information that is available before new data or observations are taken into account.
Random variables
Prior probability
A likelihood function
Parameter
48. A numerical measure that describes an aspect of a population.
Parameter
Step 1 of a statistical experiment
inferential statistics
Variability
49. A numerical measure that describes an aspect of a sample.
The variance of a random variable
A Statistical parameter
Statistic
Sampling
50. Where the null hypothesis is falsely rejected giving a 'false positive'.
A sample
Type I errors
Bias
Count data