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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.
If you are not ready to take this test, you can
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 the result of applying a statistical algorithm to a data set. It can also be described as an observable random variable.
A probability space
Valid measure
A statistic
Dependent Selection
2. (e.g. ? - b) are commonly used to denote unknown parameters (population parameters).
That is the median value
s-algebras
Greek letters
The sample space
3. Cov[X - Y] :
covariance of X and Y
An event
Conditional probability
Prior probability
4. There are four main levels of measurement used in statistics: Each of these have different degrees of usefulness in statistical research.
Correlation coefficient
nominal - ordinal - interval - and ratio
Simple random sample
categorical variables
5. Have meaningful distances between measurements defined - but the zero value is arbitrary (as in the case with longitude and temperature measurements in Celsius or Fahrenheit)
Probability and statistics
Interval measurements
Experimental and observational studies
Kurtosis
6. A numerical measure that assesses the strength of a linear relationship between two variables.
Correlation coefficient
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
Kurtosis
Marginal distribution
7. 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.
Parameter - or 'statistical parameter'
Conditional probability
Statistics
Type II errors
8. When info. in a contingency table is re-organized into more or less categories - relationships seen can change or reverse.
9. The probability of correctly detecting a false null hypothesis.
Power of a test
Average and arithmetic mean
The variance of a random variable
the population mean
10. Statistical methods can be used for summarizing or describing a collection of data; this is called
A sampling distribution
A Random vector
descriptive statistics
Power of a test
11. 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
Sampling Distribution
Inferential statistics
Pairwise independence
Statistic
12. Is often denoted by placing a caret over the corresponding symbol - e.g. - pronounced 'theta hat'.
Interval measurements
An estimate of a parameter
the population mean
Treatment
13. 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.
A Distribution function
Atomic event
Sample space
Descriptive
14. 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'
Conditional probability
Valid measure
Estimator
Step 2 of a statistical experiment
15. Is the length of the smallest interval which contains all the data.
Sampling frame
Greek letters
the population mean
The Range
16. 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.
the population correlation
Simple random sample
Inferential statistics
Sampling
17. A variable has a value or numerical measurement for which operations such as addition or averaging make sense.
Quantitative variable
A Probability measure
A Distribution function
Power of a test
18.
Divide the sum by the number of values.
the population mean
Independence or Statistical independence
An Elementary event
19. Any specific experimental condition applied to the subjects
Treatment
f(z) - and its cdf by F(z).
Simple random sample
A population or statistical population
20. 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
the population mean
An experimental study
inferential statistics
Inferential
21. 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.
A Distribution function
Conditional distribution
Residuals
the population cumulants
22. 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.
Greek letters
Average and arithmetic mean
Marginal distribution
Individual
23. A numerical measure that describes an aspect of a population.
Alpha value (Level of Significance)
Likert scale
Type I errors & Type II errors
Parameter
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
A probability space
Statistic
Correlation
Probability
25. The collection of all possible outcomes in an experiment.
Sample space
Mutual independence
Joint probability
Ordinal measurements
26. Statistics involve methods of organizing - picturing - and summarizing information from samples or population.
Descriptive
Variability
nominal - ordinal - interval - and ratio
Coefficient of determination
27. Rejecting a true null hypothesis.
descriptive statistics
Skewness
Type 1 Error
Statistical dispersion
28. The result of a Bayesian analysis that encapsulates the combination of prior beliefs or information with observed data
Posterior probability
Law of Parsimony
Marginal probability
The Mean of a random variable
29. Where the null hypothesis fails to be rejected and an actual difference between populations is missed giving a 'false negative'.
Parameter - or 'statistical parameter'
Marginal distribution
Joint distribution
Type II errors
30. Some commonly used symbols for sample statistics
An event
Probability density functions
The Range
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
31. Working from a null hypothesis two basic forms of error are recognized:
the population cumulants
Type I errors & Type II errors
Statistical adjustment
Probability density functions
32. Are written in corresponding lower case letters. For example x1 - x2 - ... - xn could be a sample corresponding to the random variable X.
Experimental and observational studies
Particular realizations of a random variable
Quantitative variable
hypothesis
33. Is a parameter that indexes a family of probability distributions.
the population correlation
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
A Statistical parameter
An experimental study
34. In the long run - as the sample size increases - the relative frequencies of outcomes approach to the theoretical probability.
Law of Large Numbers
The sample space
A data point
A population or statistical population
35. Failing to reject a false null hypothesis.
Step 1 of a statistical experiment
A Random vector
Type 2 Error
experimental studies and observational studies.
36. (also called statistical variability) is a measure of how diverse some data is. It can be expressed by the variance or the standard deviation.
covariance of X and Y
Probability density
Statistical dispersion
s-algebras
37. The probability of the observed value or something more extreme under the assumption that the null hypothesis is true.
A data point
P-value
Joint distribution
Conditional distribution
38. 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
Observational study
The average - or arithmetic mean
the population cumulants
A likelihood function
39. The probability distribution of a sample statistic based on all the possible simple random samples of the same size from a population.
Individual
Type 2 Error
Sampling Distribution
A data set
40. 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.
Count data
experimental studies and observational studies.
Kurtosis
applied statistics
41. The proportion of the explained variation by a linear regression model in the total variation.
s-algebras
Descriptive statistics
Standard error
Coefficient of determination
42. To find the average - or arithmetic mean - of a set of numbers:
Interval measurements
Qualitative variable
Divide the sum by the number of values.
Cumulative distribution functions
43. A numerical measure that describes an aspect of a sample.
A population or statistical population
Binomial experiment
A random variable
Statistic
44. Is data arising from counting that can take only non-negative integer values.
Sampling
Ratio measurements
Conditional probability
Count data
45. 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
Confounded variables
Count data
hypotheses
Standard error
46. Is a function that gives the probability of all elements in a given space: see List of probability distributions
Law of Large Numbers
A probability distribution
Interval measurements
Atomic event
47. Consists of a number of independent trials repeated under identical conditions. On each trial - there are two possible outcomes.
Binomial experiment
The average - or arithmetic mean
Law of Large Numbers
Placebo effect
48. A data value that falls outside the overall pattern of the graph.
Prior probability
Sampling
Outlier
Seasonal effect
49. (or multivariate random variable) is a vector whose components are random variables on the same probability space.
Valid measure
the sample or population mean
A Random vector
Statistic
50. Ratio and interval measurements which can be either discrete or continuous - due to their numerical nature are grouped together as
hypothesis
The Expected value
quantitative variables
Likert scale