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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. Var[X] :
Probability and statistics
the population mean
variance of X
The standard deviation
2. Two variables such that their effects on the response variable cannot be distinguished from each other.
Beta value
Greek letters
Ordinal measurements
Confounded variables
3. 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.
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
A population or statistical population
Interval measurements
The Covariance between two random variables X and Y - with expected values E(X) =
4. Consists of a number of independent trials repeated under identical conditions. On each trial - there are two possible outcomes.
Type II errors
Estimator
That is the median value
Binomial experiment
5. A pairwise independent collection of random variables is a set of random variables any two of which are independent.
That is the median value
Sampling Distribution
Type I errors
Pairwise independence
6. ?
Bias
That value is the median value
the population correlation
hypothesis
7. 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
Probability
Credence
Statistical inference
Probability density
8. (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
Probability density functions
Statistical inference
Beta value
9. Is a sample space over which a probability measure has been defined.
A probability space
Seasonal effect
the population mean
A Distribution function
10. Is a parameter that indexes a family of probability distributions.
Correlation coefficient
methods of least squares
Sample space
A Statistical parameter
11. Is its expected value. The mean (or sample mean of a data set is just the average value.
experimental studies and observational studies.
Interval measurements
A random variable
The Mean of a random variable
12. 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)
Interval measurements
The Covariance between two random variables X and Y - with expected values E(X) =
Binomial experiment
A statistic
13. Is a sample and the associated data points.
Individual
A data set
the sample or population mean
Qualitative variable
14. 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
Treatment
Trend
Correlation coefficient
Skewness
15. Some commonly used symbols for population parameters
The Range
the population cumulants
A Statistical parameter
the population mean
16. 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.
Step 2 of a statistical experiment
A likelihood function
A Random vector
Independent Selection
17. 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.
Null hypothesis
the population mean
Kurtosis
Trend
18. Is data arising from counting that can take only non-negative integer values.
Quantitative variable
Count data
A Distribution function
The variance of a random variable
19. 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
applied statistics
Power of a test
The median value
Probability density
20. A measurement such that the random error is small
Type II errors
That is the median value
Reliable measure
Independence or Statistical independence
21. 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
Individual
Simulation
Qualitative variable
Descriptive statistics
22. (pdfs) and probability mass functions are denoted by lower case letters - e.g. f(x).
The Expected value
the population mean
Probability and statistics
Probability density functions
23. 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.
Lurking variable
Particular realizations of a random variable
Simple random sample
Reliable measure
24. When you have two or more competing models - choose the simpler of the two models.
Law of Parsimony
the population mean
the population mean
Marginal probability
25. In Bayesian inference - this represents prior beliefs or other information that is available before new data or observations are taken into account.
Likert scale
applied statistics
Prior probability
Inferential
26. The standard deviation of a sampling distribution.
Particular realizations of a random variable
Inferential statistics
Standard error
Beta value
27. Many statistical methods seek to minimize the mean-squared error - and these are called
Average and arithmetic mean
Trend
methods of least squares
Statistical inference
28. Is the probability of an event - ignoring any information about other events. The marginal probability of A is written P(A). Contrast with conditional probability.
Conditional distribution
The Range
Marginal probability
Residuals
29. Have imprecise differences between consecutive values - but have a meaningful order to those values
Ordinal measurements
Marginal probability
Skewness
The Covariance between two random variables X and Y - with expected values E(X) =
30. Are written in corresponding lower case letters. For example x1 - x2 - ... - xn could be a sample corresponding to the random variable X.
Nominal measurements
Particular realizations of a random variable
Beta value
categorical variables
31. ?r
the population cumulants
Joint probability
Conditional distribution
An experimental study
32. 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.
Dependent Selection
Statistic
P-value
Variable
33. Describes a characteristic of an individual to be measured or observed.
The sample space
The Range
Conditional distribution
Variable
34. 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
Nominal measurements
Sampling Distribution
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
hypothesis
35. 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.
That value is the median value
Sampling
Credence
Divide the sum by the number of values.
36. 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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37. 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.
Pairwise independence
The median value
Law of Parsimony
An experimental study
38. Cov[X - Y] :
covariance of X and Y
descriptive statistics
Variability
A data set
39. (also called statistical variability) is a measure of how diverse some data is. It can be expressed by the variance or the standard deviation.
Statistical dispersion
Trend
Simple random sample
Credence
40. The errors - or difference between the estimated response y^i and the actual measured response yi - collectively
Statistical inference
Dependent Selection
Residuals
covariance of X and Y
41. (e.g. ? - b) are commonly used to denote unknown parameters (population parameters).
A random variable
Lurking variable
Alpha value (Level of Significance)
Greek letters
42. 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
f(z) - and its cdf by F(z).
Step 3 of a statistical experiment
Alpha value (Level of Significance)
Step 2 of a statistical experiment
43. 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
Beta value
applied statistics
An estimate of a parameter
inferential statistics
44. The probability of the observed value or something more extreme under the assumption that the null hypothesis is true.
Simulation
P-value
The standard deviation
Inferential statistics
45. A variable has a value or numerical measurement for which operations such as addition or averaging make sense.
Average and arithmetic mean
Descriptive
Outlier
Quantitative variable
46. A variable describes an individual by placing the individual into a category or a group.
Step 3 of a statistical experiment
Qualitative variable
A sampling distribution
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
47. S^2
Estimator
the population variance
Variability
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
48. 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
Sampling
Probability and statistics
expected value of X
Placebo effect
49. 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.
The standard deviation
Seasonal effect
The variance of a random variable
Standard error
50. The collection of all possible outcomes in an experiment.
Coefficient of determination
Independent Selection
Reliable measure
Sample space