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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.
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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. 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
Pairwise independence
A data set
quantitative variables
Probability and statistics
2. Working from a null hypothesis two basic forms of error are recognized:
Type I errors & Type II errors
Divide the sum by the number of values.
Statistical dispersion
hypothesis
3. Cov[X - Y] :
covariance of X and Y
Sampling
Power of a test
Ratio measurements
4. Data are gathered and correlations between predictors and response are investigated.
methods of least squares
observational study
Independent Selection
Sampling frame
5. Probability of rejecting a true null hypothesis.
Alpha value (Level of Significance)
Treatment
the population mean
A random variable
6. Of a group of numbers is the center point of all those number values.
Qualitative variable
Sampling
Atomic event
The average - or arithmetic mean
7. 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
Average and arithmetic mean
Conditional probability
The average - or arithmetic mean
8. Failing to reject a false null hypothesis.
Step 3 of a statistical experiment
Type 2 Error
A Probability measure
An event
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.
Conditional distribution
variance of X
An experimental study
covariance of X and Y
10. When you have two or more competing models - choose the simpler of the two models.
inferential statistics
Bias
Law of Parsimony
Binomial experiment
11. Another name for elementary event.
Atomic event
Step 3 of a statistical experiment
descriptive statistics
quantitative variables
12. Where the null hypothesis is falsely rejected giving a 'false positive'.
Binary data
Type I errors
Descriptive statistics
Statistical inference
13. 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
f(z) - and its cdf by F(z).
The Covariance between two random variables X and Y - with expected values E(X) =
the sample or population mean
experimental studies and observational studies.
14. 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.
Credence
The median value
The Mean of a random variable
Sampling
15. Is often denoted by placing a caret over the corresponding symbol - e.g. - pronounced 'theta hat'.
Reliable measure
An estimate of a parameter
Marginal probability
Independent Selection
16. Are simply two different terms for the same thing. Add the given values
Particular realizations of a random variable
An estimate of a parameter
Average and arithmetic mean
Block
17. A pairwise independent collection of random variables is a set of random variables any two of which are independent.
Pairwise independence
Variable
categorical variables
Type I errors
18. ?
Power of a test
the population correlation
P-value
Type 1 Error
19. 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
Mutual independence
Average and arithmetic mean
hypotheses
20. A consistent - repeated deviation of the sample statistic from the population parameter in the same direction when many samples are taken.
experimental studies and observational studies.
A Random vector
Bias
Confounded variables
21. Is data arising from counting that can take only non-negative integer values.
Skewness
Cumulative distribution functions
Count data
Quantitative variable
22. 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.
Independent Selection
That is the median value
A statistic
Descriptive
23. The result of a Bayesian analysis that encapsulates the combination of prior beliefs or information with observed data
Marginal distribution
Ratio measurements
Posterior probability
Probability density
24. (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
Variable
Observational study
The Expected value
Greek letters
25. Gives the probability distribution for a continuous random variable.
Qualitative variable
Interval measurements
A probability density function
the sample or population mean
26. 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.
P-value
The Mean of a random variable
the sample or population mean
Seasonal effect
27. Are usually written in upper case roman letters: X - Y - etc.
Descriptive
Random variables
Likert scale
Conditional probability
28. Consists of a number of independent trials repeated under identical conditions. On each trial - there are two possible outcomes.
Binomial experiment
Dependent Selection
Confounded variables
Binary data
29. Any specific experimental condition applied to the subjects
Treatment
nominal - ordinal - interval - and ratio
Probability density functions
variance of X
30. Some commonly used symbols for sample statistics
Outlier
hypothesis
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
Joint distribution
31. 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.
Probability and statistics
A random variable
Step 3 of a statistical experiment
That is the median value
32. The objects described by a set of data: person (animal) - place - and - thing. (SUBJECTS)
variance of X
Individual
Likert scale
Probability density functions
33. Probability of accepting a false null hypothesis.
Type II errors
experimental studies and observational studies.
Beta value
A data point
34. The probability of correctly detecting a false null hypothesis.
A statistic
The standard deviation
Power of a test
The average - or arithmetic mean
35. The collection of all possible outcomes in an experiment.
Sample space
Bias
Binomial experiment
Sampling frame
36. To find the median value of a set of numbers: Arrange the numbers in numerical order. Locate the two middle numbers in the list. Find the average of those two middle values.
Sampling Distribution
That value is the median value
experimental studies and observational studies.
A probability density function
37. Is its expected value. The mean (or sample mean of a data set is just the average value.
Residuals
Nominal measurements
The Mean of a random variable
Statistics
38. Error also refers to the extent to which individual observations in a sample differ from a central value - such as
the sample or population mean
Outlier
Lurking variable
Inferential statistics
39. A subjective estimate of probability.
Conditional probability
Random variables
Marginal distribution
Credence
40. Have no meaningful rank order among values.
The median value
Nominal measurements
the population variance
Marginal distribution
41. 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
An event
Confounded variables
Step 2 of a statistical experiment
The Expected value
42. Long-term upward or downward movement over time.
Statistical dispersion
Trend
Seasonal effect
Type I errors & Type II errors
43. A data value that falls outside the overall pattern of the graph.
A Distribution function
f(z) - and its cdf by F(z).
Treatment
Outlier
44. There are four main levels of measurement used in statistics: Each of these have different degrees of usefulness in statistical research.
Reliable measure
The variance of a random variable
nominal - ordinal - interval - and ratio
inferential statistics
45. The errors - or difference between the estimated response y^i and the actual measured response yi - collectively
Valid measure
Residuals
Statistical adjustment
Null hypothesis
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
applied statistics
Mutual independence
Inferential statistics
Beta value
47. 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
covariance of X and Y
Probability density
the sample or population mean
Valid measure
48. Is the set of possible outcomes of an experiment. For example - the sample space for rolling a six-sided die will be {1 - 2 - 3 - 4 - 5 - 6}.
Type 1 Error
The Covariance between two random variables X and Y - with expected values E(X) =
Variable
The sample space
49. When there is an even number of values...
Sampling Distribution
Quantitative variable
Posterior probability
That is the median value
50. (or atomic event) is an event with only one element. For example - when pulling a card out of a deck - 'getting the jack of spades' is an elementary event - while 'getting a king or an ace' is not.
Estimator
An Elementary event
Correlation
A Probability measure