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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
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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. In Bayesian inference - this represents prior beliefs or other information that is available before new data or observations are taken into account.
Prior probability
A probability space
s-algebras
Beta value
2. The proportion of the explained variation by a linear regression model in the total variation.
Estimator
Particular realizations of a random variable
hypotheses
Coefficient of determination
3. 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
Marginal distribution
Descriptive statistics
the population mean
Step 3 of a statistical experiment
4. A group of individuals sharing some common features that might affect the treatment.
A statistic
the population mean
Block
Statistical adjustment
5. S^2
Observational study
Descriptive statistics
Posterior probability
the population variance
6. A consistent - repeated deviation of the sample statistic from the population parameter in the same direction when many samples are taken.
Bias
Simulation
Divide the sum by the number of values.
Seasonal effect
7. Is its expected value. The mean (or sample mean of a data set is just the average value.
Cumulative distribution functions
A Probability measure
Step 1 of a statistical experiment
The Mean of a random variable
8. (or just likelihood) is a conditional probability function considered a function of its second argument with its first argument held fixed. For example - imagine pulling a numbered ball with the number k from a bag of n balls - numbered 1 to n. Then
An event
The sample space
A likelihood function
Conditional probability
9. Is the probability distribution - under repeated sampling of the population - of a given statistic.
Coefficient of determination
A sampling distribution
Skewness
Likert scale
10. 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
A population or statistical population
the population mean
Confounded variables
inferential statistics
11. The objects described by a set of data: person (animal) - place - and - thing. (SUBJECTS)
Individual
An estimate of a parameter
Simulation
the population mean
12. 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
The standard deviation
Step 3 of a statistical experiment
Type 1 Error
Quantitative variable
13. (e.g. ? - b) are commonly used to denote unknown parameters (population parameters).
Power of a test
Step 3 of a statistical experiment
Block
Greek letters
14. Another name for elementary event.
Type 2 Error
Type I errors
Posterior probability
Atomic event
15. Where the null hypothesis is falsely rejected giving a 'false positive'.
Type I errors
The average - or arithmetic mean
Statistical adjustment
Statistic
16. Also called correlation coefficient - is a numeric measure of the strength of linear relationship between two random variables (one can use it to quantify - for example - how shoe size and height are correlated in the population). An example is the P
Average and arithmetic mean
Binomial experiment
Independent Selection
Correlation
17. 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 sample space
Independent Selection
Variability
s-algebras
18. A numerical measure that describes an aspect of a population.
An Elementary event
Parameter
Lurking variable
Correlation coefficient
19. E[X] :
Lurking variable
expected value of X
Conditional distribution
A population or statistical population
20. Many statistical methods seek to minimize the mean-squared error - and these are called
A Statistical parameter
Bias
Statistical dispersion
methods of least squares
21. Of a group of numbers is the center point of all those number values.
The Mean of a random variable
Conditional distribution
The average - or arithmetic mean
Outlier
22. 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.
Count data
s-algebras
Trend
An experimental study
23. Is a sample and the associated data points.
Step 2 of a statistical experiment
Ordinal measurements
A data set
Estimator
24. 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'
Marginal probability
Conditional distribution
Statistics
25. Is that part of a population which is actually observed.
A probability distribution
Quantitative variable
A random variable
A sample
26. A measure that is relevant or appropriate as a representation of that property.
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
the sample or population mean
Valid measure
Statistical dispersion
27. 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.
Sampling
Type II errors
descriptive statistics
Particular realizations of a random variable
28. Two variables such that their effects on the response variable cannot be distinguished from each other.
Confounded variables
Valid measure
Greek letters
Coefficient of determination
29. The collection of all possible outcomes in an experiment.
Sample space
Dependent Selection
Divide the sum by the number of values.
Prior probability
30. ?
P-value
An experimental study
the population correlation
A probability density function
31. Is a sample space over which a probability measure has been defined.
Posterior probability
A probability space
Average and arithmetic mean
the population mean
32. Long-term upward or downward movement over time.
Correlation
Placebo effect
That value is the median value
Trend
33. 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)
Inferential
Interval measurements
A probability space
applied statistics
34. Is the probability of two events occurring together. The joint probability of A and B is written P(A and B) or P(A - B).
Valid measure
Simple random sample
Inferential statistics
Joint probability
35. Changes over time that show a regular periodicity in the data where regular means over a fixed interval; the time between repetitions is called the period.
Power of a test
Quantitative variable
Seasonal effect
Kurtosis
36. 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.
Marginal distribution
the population mean
The variance of a random variable
Ordinal measurements
37. The probability of correctly detecting a false null hypothesis.
An Elementary event
Particular realizations of a random variable
Power of a test
Sampling
38. 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.
Variable
the population cumulants
Conditional distribution
Trend
39. 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
A Statistical parameter
Cumulative distribution functions
hypothesis
A sampling distribution
40. A subjective estimate of probability.
the population cumulants
Law of Large Numbers
Credence
applied statistics
41. Probability of accepting a false null hypothesis.
categorical variables
Probability
Beta value
A data point
42. In the long run - as the sample size increases - the relative frequencies of outcomes approach to the theoretical probability.
Type I errors & Type II errors
Law of Large Numbers
Simulation
Inferential
43. 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.
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
Particular realizations of a random variable
Lurking variable
Interval measurements
44. 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
Particular realizations of a random variable
Probability
hypothesis
Simpson's Paradox
45. There are four main levels of measurement used in statistics: Each of these have different degrees of usefulness in statistical research.
Statistics
Block
nominal - ordinal - interval - and ratio
Simpson's Paradox
46. 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
Bias
Individual
Type 2 Error
47. Probability of rejecting a true null hypothesis.
Alpha value (Level of Significance)
Simulation
Null hypothesis
A statistic
48. When there is an even number of values...
Placebo effect
Greek letters
That is the median value
s-algebras
49. 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
Seasonal effect
Type I errors
Descriptive statistics
50. 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
hypothesis
Type II errors
Type I errors