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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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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. 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
Bias
A sampling distribution
Probability
Reliable measure
2. Is the most commonly used measure of statistical dispersion. It is the square root of the variance - and is generally written s (sigma).
That value is the median value
The standard deviation
Conditional probability
observational study
3. 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.
Joint probability
Lurking variable
A Statistical parameter
An Elementary event
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
A random variable
Law of Large Numbers
A probability density function
Step 3 of a statistical experiment
5. When you have two or more competing models - choose the simpler of the two models.
Law of Parsimony
Step 2 of a statistical experiment
Block
Probability
6. 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.
Greek letters
Statistical inference
categorical variables
Prior probability
7. To find the average - or arithmetic mean - of a set of numbers:
Divide the sum by the number of values.
A sampling distribution
Statistics
The Range
8. 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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9. 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.
An experimental study
Parameter
Likert scale
the population mean
10. A numerical measure that describes an aspect of a population.
Parameter
Trend
Type I errors & Type II errors
Random variables
11. In particular - the pdf of the standard normal distribution is denoted by
The Range
Experimental and observational studies
Descriptive
f(z) - and its cdf by F(z).
12. 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.
Kurtosis
Statistics
Count data
Binomial experiment
13. To prove the guiding theory further - these predictions are tested as well - as part of the scientific method. If the inference holds true - then the descriptive statistics of the new data increase the soundness of that
Statistic
A Statistical parameter
Sampling
hypothesis
14. 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.
The Expected value
An experimental study
The variance of a random variable
Descriptive statistics
15. Are written in corresponding lower case letters. For example x1 - x2 - ... - xn could be a sample corresponding to the random variable X.
Particular realizations of a random variable
A data point
Statistical adjustment
Coefficient of determination
16. Is data that can take only two values - usually represented by 0 and 1.
the population correlation
Variable
Binary data
the sample or population mean
17. Is a process of selecting observations to obtain knowledge about a population. There are many methods to choose on which sample to do the observations.
Probability density
Sampling
A Statistical parameter
An event
18. E[X] :
Pairwise independence
expected value of X
Ratio measurements
variance of X
19. 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
Random variables
The Mean of a random variable
Probability and statistics
Skewness
20. In Bayesian inference - this represents prior beliefs or other information that is available before new data or observations are taken into account.
Average and arithmetic mean
Placebo effect
The variance of a random variable
Prior probability
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
Probability and statistics
Conditional probability
Bias
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
22. In the long run - as the sample size increases - the relative frequencies of outcomes approach to the theoretical probability.
Type I errors
The Covariance between two random variables X and Y - with expected values E(X) =
Trend
Law of Large Numbers
23. 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
Probability density
A population or statistical population
Divide the sum by the number of values.
Type 1 Error
24. The standard deviation of a sampling distribution.
An experimental study
The variance of a random variable
Standard error
Sampling
25. A consistent - repeated deviation of the sample statistic from the population parameter in the same direction when many samples are taken.
Statistical dispersion
Bias
P-value
expected value of X
26. A subjective estimate of probability.
Average and arithmetic mean
hypothesis
Beta value
Credence
27. The probability distribution of a sample statistic based on all the possible simple random samples of the same size from a population.
applied statistics
Ordinal measurements
Residuals
Sampling Distribution
28.
the population mean
Simpson's Paradox
A likelihood function
Statistical adjustment
29. 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
Statistical adjustment
Standard error
Observational study
categorical variables
30. 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
A probability space
A sampling distribution
Statistics
31. Is defined as the expected value of random variable (X -
s-algebras
The Covariance between two random variables X and Y - with expected values E(X) =
Ordinal measurements
Posterior probability
32. (or multivariate random variable) is a vector whose components are random variables on the same probability space.
A Random vector
covariance of X and Y
Type I errors & Type II errors
The standard deviation
33. 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
Posterior probability
Inferential statistics
Probability density functions
the population variance
34. A measure that is relevant or appropriate as a representation of that property.
Valid measure
A Distribution function
Ordinal measurements
hypothesis
35. Statistics involve methods of using information from a sample to draw conclusions regarding the population.
variance of X
An Elementary event
Type II errors
Inferential
36. 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.
Statistics
A Random vector
Probability
categorical variables
37. 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
Credence
The average - or arithmetic mean
Interval measurements
Mutual independence
38. A group of individuals sharing some common features that might affect the treatment.
nominal - ordinal - interval - and ratio
Type II errors
Placebo effect
Block
39. 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
Step 1 of a statistical experiment
Parameter - or 'statistical parameter'
Ordinal measurements
Correlation coefficient
40. Error also refers to the extent to which individual observations in a sample differ from a central value - such as
Step 2 of a statistical experiment
the sample or population mean
Greek letters
Binomial experiment
41. S^2
the population variance
An estimate of a parameter
quantitative variables
Type 1 Error
42. Is a sample and the associated data points.
A data set
Statistical inference
Ordinal measurements
The Mean of a random variable
43. Is the length of the smallest interval which contains all the data.
The median value
Probability density
Ratio measurements
The Range
44. 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.
methods of least squares
Nominal measurements
Experimental and observational studies
Probability
45. 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.
Estimator
the population mean
the sample or population mean
Sampling frame
46. 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.
Mutual independence
Credence
Conditional distribution
The sample space
47. The errors - or difference between the estimated response y^i and the actual measured response yi - collectively
experimental studies and observational studies.
Residuals
Divide the sum by the number of values.
Prior probability
48. Failing to reject a false null hypothesis.
Average and arithmetic mean
Particular realizations of a random variable
Divide the sum by the number of values.
Type 2 Error
49. Many statistical methods seek to minimize the mean-squared error - and these are called
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Inferential statistics
Observational study
methods of least squares
50. Is often denoted by placing a caret over the corresponding symbol - e.g. - pronounced 'theta hat'.
Sampling
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
An estimate of a parameter
An Elementary event