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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. Given two random variables X and Y - the joint distribution of X and Y is the probability distribution of X and Y together.
Seasonal effect
Joint distribution
the population variance
Nominal measurements
2. 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.
The Mean of a random variable
P-value
A probability distribution
An experimental study
3. A pairwise independent collection of random variables is a set of random variables any two of which are independent.
Seasonal effect
Joint probability
methods of least squares
Pairwise independence
4. There are four main levels of measurement used in statistics: Each of these have different degrees of usefulness in statistical research.
variance of X
nominal - ordinal - interval - and ratio
Credence
Particular realizations of a random variable
5. Have no meaningful rank order among values.
Step 2 of a statistical experiment
Beta value
Nominal measurements
expected value of X
6. Occurs when a subject receives no treatment - but (incorrectly) believes he or she is in fact receiving treatment and responds favorably.
Ratio measurements
Placebo effect
P-value
A likelihood function
7. 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
Inferential
s-algebras
observational study
8. 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.
Type 2 Error
Skewness
A Distribution function
Seasonal effect
9. Used to reduce bias - this measure weights the more relevant information higher than less relevant info.
Treatment
A Probability measure
Type II errors
Statistical adjustment
10. Have both a meaningful zero value and the distances between different measurements defined; they provide the greatest flexibility in statistical methods that can be used for analyzing the data
A Probability measure
Ratio measurements
Inferential
Dependent Selection
11. 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.
A sampling distribution
Greek letters
Type II errors
Statistics
12. The proportion of the explained variation by a linear regression model in the total variation.
Correlation
Coefficient of determination
Joint distribution
Divide the sum by the number of values.
13. Some commonly used symbols for population parameters
Reliable measure
Nominal measurements
Particular realizations of a random variable
the population mean
14. Gives the probability of events in a probability space.
A Probability measure
Qualitative variable
Variability
Estimator
15. Is a sample space over which a probability measure has been defined.
Divide the sum by the number of values.
A probability space
Null hypothesis
The Range
16. Working from a null hypothesis two basic forms of error are recognized:
Inferential statistics
Type I errors & Type II errors
the sample or population mean
Step 1 of a statistical experiment
17. A list of individuals from which the sample is actually selected.
Placebo effect
Alpha value (Level of Significance)
Cumulative distribution functions
Sampling frame
18. 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
Trend
The Expected value
Nominal measurements
Inferential statistics
19. Consists of a number of independent trials repeated under identical conditions. On each trial - there are two possible outcomes.
A probability density function
the population cumulants
Binomial experiment
An estimate of a parameter
20. E[X] :
expected value of X
Experimental and observational studies
The Mean of a random variable
Treatment
21. 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.
Mutual independence
Sampling
Qualitative variable
Reliable measure
22. Some commonly used symbols for sample statistics
Bias
Reliable measure
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
expected value of X
23. A numerical measure that assesses the strength of a linear relationship between two variables.
Correlation coefficient
Sampling Distribution
inferential statistics
The Range
24. (pdfs) and probability mass functions are denoted by lower case letters - e.g. f(x).
Inferential
Ordinal measurements
Probability density functions
Probability density
25. In the long run - as the sample size increases - the relative frequencies of outcomes approach to the theoretical probability.
Average and arithmetic mean
Law of Large Numbers
Ordinal measurements
Variability
26.
Sampling
the population mean
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
Parameter
27. Is its expected value. The mean (or sample mean of a data set is just the average value.
covariance of X and Y
The Mean of a random variable
Atomic event
The Covariance between two random variables X and Y - with expected values E(X) =
28. A data value that falls outside the overall pattern of the graph.
An experimental study
Outlier
Skewness
Parameter
29. 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
A Statistical parameter
Independence or Statistical independence
Skewness
Power of a test
30. Are simply two different terms for the same thing. Add the given values
Variable
Type I errors
Average and arithmetic mean
Qualitative variable
31. 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.
Simple random sample
s-algebras
A data point
That value is the median value
32. Have imprecise differences between consecutive values - but have a meaningful order to those values
Ordinal measurements
Joint probability
Alpha value (Level of Significance)
The Range
33. Var[X] :
Statistical adjustment
Null hypothesis
Inferential statistics
variance of X
34. Ratio and interval measurements which can be either discrete or continuous - due to their numerical nature are grouped together as
Interval measurements
the sample or population mean
The variance of a random variable
quantitative variables
35. Is often denoted by placing a caret over the corresponding symbol - e.g. - pronounced 'theta hat'.
The average - or arithmetic mean
Qualitative variable
An estimate of a parameter
Type I errors & Type II errors
36. 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).
The Expected value
Sample space
Joint probability
A population or statistical population
37. Descriptive statistics and inferential statistics (a.k.a. - predictive statistics) together comprise
The variance of a random variable
Sampling
applied statistics
Kurtosis
38. Can refer either to a sample not being representative of the population - or to the difference between the expected value of an estimator and the true value.
Observational study
Probability and statistics
Bias
Individual
39. 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
Step 3 of a statistical experiment
Joint probability
Sampling
40. 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
s-algebras
Probability density
hypothesis
nominal - ordinal - interval - and ratio
41. 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
Variability
Lurking variable
Conditional distribution
Step 3 of a statistical experiment
42. Is defined as the expected value of random variable (X -
The Covariance between two random variables X and Y - with expected values E(X) =
Bias
Joint probability
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
43. Statistics involve methods of using information from a sample to draw conclusions regarding the population.
Individual
the population variance
Inferential
Parameter - or 'statistical parameter'
44. ?r
An experimental study
Confounded variables
the population cumulants
Qualitative variable
45. 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 random variable
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
Outlier
Null hypothesis
46. 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) =
A Probability measure
methods of least squares
47. When you have two or more competing models - choose the simpler of the two models.
Nominal measurements
Sampling
Law of Parsimony
A Random vector
48. 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 Statistical parameter
Step 2 of a statistical experiment
Step 3 of a statistical experiment
the population variance
49. Describes the spread in the values of the sample statistic when many samples are taken.
Nominal measurements
hypotheses
The Range
Variability
50. The probability distribution of a sample statistic based on all the possible simple random samples of the same size from a population.
Independent Selection
Sampling Distribution
Count data
Dependent Selection