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CLEP General Mathematics: Probability And Statistics
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Answer 50 questions in 15 minutes.
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Match each statement with the correct term.
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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 the result of applying a statistical algorithm to a data set. It can also be described as an observable random variable.
Step 2 of a statistical experiment
Independent Selection
the population mean
A statistic
2. 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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3. When there is an even number of values...
That value is the median value
Independence or Statistical independence
Atomic event
That is the median value
4. 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
A statistic
inferential statistics
Null hypothesis
Step 2 of a statistical experiment
5. 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
Probability density
Individual
hypothesis
Descriptive statistics
6. (pdfs) and probability mass functions are denoted by lower case letters - e.g. f(x).
Parameter
Probability density functions
Qualitative variable
A sampling distribution
7. There are four main levels of measurement used in statistics: Each of these have different degrees of usefulness in statistical research.
Credence
An event
Seasonal effect
nominal - ordinal - interval - and ratio
8. 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.
A Statistical parameter
The variance of a random variable
A random variable
Random variables
9. Describes the spread in the values of the sample statistic when many samples are taken.
variance of X
Variability
Quantitative variable
A data set
10. 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
Binomial experiment
Outlier
Power of a test
11. 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
A Probability measure
Sampling Distribution
experimental studies and observational studies.
Pairwise independence
12. Are usually written in upper case roman letters: X - Y - etc.
Inferential statistics
Lurking variable
Random variables
Joint probability
13. The probability of the observed value or something more extreme under the assumption that the null hypothesis is true.
P-value
Placebo effect
Parameter
Power of a test
14. 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.
s-algebras
Type I errors
A sample
Simple random sample
15. Is the most commonly used measure of statistical dispersion. It is the square root of the variance - and is generally written s (sigma).
Statistic
Ratio measurements
The standard deviation
the sample or population mean
16. 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.
Sampling frame
A population or statistical population
observational study
The variance of a random variable
17. The proportion of the explained variation by a linear regression model in the total variation.
Residuals
Conditional probability
A data set
Coefficient of determination
18. ?
Null hypothesis
the population correlation
The median value
Joint probability
19. 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.
Nominal measurements
Ordinal measurements
An Elementary event
Lurking variable
20. 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.
Greek letters
the population mean
Dependent Selection
Divide the sum by the number of values.
21. Are written in corresponding lower case letters. For example x1 - x2 - ... - xn could be a sample corresponding to the random variable X.
The Range
Individual
Simpson's Paradox
Particular realizations of a random variable
22. 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.
Simple random sample
Confounded variables
A Distribution function
nominal - ordinal - interval - and ratio
23. The standard deviation of a sampling distribution.
Valid measure
Statistic
Standard error
Sampling
24. 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
Step 3 of a statistical experiment
Probability
Interval measurements
Correlation coefficient
25. Probability of rejecting a true null hypothesis.
Skewness
Alpha value (Level of Significance)
Observational study
An estimate of a parameter
26. 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.
experimental studies and observational studies.
Type II errors
Average and arithmetic mean
Statistics
27. Statistical methods can be used for summarizing or describing a collection of data; this is called
descriptive statistics
the sample or population mean
Treatment
Marginal probability
28. 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
Binary data
Skewness
Count data
A Distribution function
29. 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.
nominal - ordinal - interval - and ratio
A probability space
Independent Selection
A Statistical parameter
30. Rejecting a true null hypothesis.
A probability density function
The median value
Type 1 Error
Descriptive
31. Is the length of the smallest interval which contains all the data.
Sample space
Lurking variable
the sample or population mean
The Range
32. Is a sample and the associated data points.
Step 2 of a statistical experiment
Interval measurements
A population or statistical population
A data set
33. Is that part of a population which is actually observed.
Type 1 Error
A sample
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
Divide the sum by the number of values.
34. 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
Bias
Outlier
The Mean of a random variable
35. 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.
Inferential statistics
The Covariance between two random variables X and Y - with expected values E(X) =
Interval measurements
Estimator
36. (e.g. ? - b) are commonly used to denote unknown parameters (population parameters).
Dependent Selection
Greek letters
Reliable measure
The median value
37. 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
Treatment
Law of Large Numbers
categorical variables
38. Is data that can take only two values - usually represented by 0 and 1.
A random variable
Sampling
Binary data
Atomic event
39. Gives the probability distribution for a continuous random variable.
The median value
A probability density function
The variance of a random variable
A random variable
40. Have imprecise differences between consecutive values - but have a meaningful order to those values
Ordinal measurements
Probability and statistics
Sampling frame
Standard error
41. Var[X] :
Dependent Selection
Nominal measurements
variance of X
Reliable measure
42. Probability of accepting a false null hypothesis.
A Probability measure
covariance of X and Y
Beta value
Divide the sum by the number of values.
43. (or multivariate random variable) is a vector whose components are random variables on the same probability space.
the population mean
Probability density
Correlation coefficient
A Random vector
44. Is the probability distribution - under repeated sampling of the population - of a given statistic.
hypotheses
Lurking variable
A sampling distribution
the population mean
45. 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
Step 1 of a statistical experiment
Binomial experiment
Inferential statistics
Probability density
46. Long-term upward or downward movement over time.
Count data
Ratio measurements
Trend
A population or statistical population
47. S^2
Step 1 of a statistical experiment
the population variance
Correlation
Average and arithmetic mean
48. Consists of a number of independent trials repeated under identical conditions. On each trial - there are two possible outcomes.
Simulation
Lurking variable
Statistical adjustment
Binomial experiment
49. (also called statistical variability) is a measure of how diverse some data is. It can be expressed by the variance or the standard deviation.
Dependent Selection
Statistical inference
s-algebras
Statistical dispersion
50. Statistics involve methods of organizing - picturing - and summarizing information from samples or population.
A probability space
Step 3 of a statistical experiment
nominal - ordinal - interval - and ratio
Descriptive
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