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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. To find the average - or arithmetic mean - of a set of numbers:
Greek letters
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Divide the sum by the number of values.
An event
2. 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.
Likert scale
Confounded variables
A sampling distribution
Dependent Selection
3. 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.
Lurking variable
Parameter - or 'statistical parameter'
Inferential statistics
Divide the sum by the number of values.
4. 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.
Parameter - or 'statistical parameter'
the population mean
Block
A Distribution function
5. A measurement such that the random error is small
Count data
The Expected value
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Reliable measure
6. 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
Conditional distribution
Marginal distribution
methods of least squares
7. Probability of accepting a false null hypothesis.
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
Bias
Beta value
The Covariance between two random variables X and Y - with expected values E(X) =
8. 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
Residuals
Binomial experiment
A Probability measure
Skewness
9. The proportion of the explained variation by a linear regression model in the total variation.
Type 2 Error
Law of Large Numbers
The average - or arithmetic mean
Coefficient of determination
10. 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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11. (or multivariate random variable) is a vector whose components are random variables on the same probability space.
Probability density
A Random vector
Seasonal effect
Simpson's Paradox
12. Descriptive statistics and inferential statistics (a.k.a. - predictive statistics) together comprise
Joint distribution
Outlier
applied statistics
variance of X
13. Have imprecise differences between consecutive values - but have a meaningful order to those values
Bias
observational study
Ordinal measurements
Parameter
14. (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.
Inferential statistics
Individual
An Elementary event
An estimate of a parameter
15. Rejecting a true null hypothesis.
s-algebras
the population variance
hypothesis
Type 1 Error
16. Is a subset of the sample space - to which a probability can be assigned. For example - on rolling a die - 'getting a five or a six' is an event (with a probability of one third if the die is fair).
An event
the population mean
Dependent Selection
Descriptive statistics
17. Any specific experimental condition applied to the subjects
Binomial experiment
Variability
observational study
Treatment
18. ?r
the sample or population mean
Standard error
the population cumulants
A Statistical parameter
19. In Bayesian inference - this represents prior beliefs or other information that is available before new data or observations are taken into account.
Standard error
Prior probability
Sampling frame
Type 1 Error
20. When info. in a contingency table is re-organized into more or less categories - relationships seen can change or reverse.
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21. 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
Binomial experiment
Law of Parsimony
Type 1 Error
22. 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}.
Independence or Statistical independence
Placebo effect
An event
The sample space
23. The errors - or difference between the estimated response y^i and the actual measured response yi - collectively
Residuals
Correlation coefficient
Particular realizations of a random variable
A sample
24. A numerical measure that assesses the strength of a linear relationship between two variables.
Correlation coefficient
Qualitative variable
Nominal measurements
Atomic event
25. 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).
Atomic event
Joint probability
Step 3 of a statistical experiment
Confounded variables
26. 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.
A data point
Simple random sample
Beta value
nominal - ordinal - interval - and ratio
27. Is that part of a population which is actually observed.
Step 1 of a statistical experiment
A Statistical parameter
A sample
Probability and statistics
28. 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
Marginal distribution
Count data
descriptive statistics
29. Used to reduce bias - this measure weights the more relevant information higher than less relevant info.
descriptive statistics
A statistic
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
Statistical adjustment
30. 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.
descriptive statistics
Seasonal effect
A sampling distribution
Marginal distribution
31. 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
Inferential statistics
Correlation
Dependent Selection
A Random vector
32. Given two random variables X and Y - the joint distribution of X and Y is the probability distribution of X and Y together.
Alpha value (Level of Significance)
Step 2 of a statistical experiment
Joint distribution
That is the median value
33. Is its expected value. The mean (or sample mean of a data set is just the average value.
The Mean of a random variable
Marginal probability
the population mean
P-value
34. Many statistical methods seek to minimize the mean-squared error - and these are called
Marginal distribution
A sample
methods of least squares
Atomic event
35. A list of individuals from which the sample is actually selected.
Probability density functions
Confounded variables
Estimator
Sampling frame
36. 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.
Ordinal measurements
Independent Selection
A Distribution function
Sampling
37. (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
Sample space
The Expected value
Individual
descriptive statistics
38. E[X] :
Kurtosis
Statistical adjustment
expected value of X
Probability
39.
Mutual independence
The Range
the population mean
Posterior probability
40. 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.
That value is the median value
Residuals
expected value of X
inferential statistics
41. In the long run - as the sample size increases - the relative frequencies of outcomes approach to the theoretical probability.
covariance of X and Y
The Expected value
Treatment
Law of Large Numbers
42. Some commonly used symbols for population parameters
the population mean
Type II errors
Prior probability
Greek letters
43. Are usually written with upper case calligraphic (e.g. F for the set of sets on which we define the probability P)
Step 3 of a statistical experiment
Descriptive
Dependent Selection
s-algebras
44. 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.
Binary data
the population variance
A Random vector
Kurtosis
45. 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
Ratio measurements
Step 2 of a statistical experiment
Standard error
Probability
46. In particular - the pdf of the standard normal distribution is denoted by
Sample space
The Expected value
Correlation
f(z) - and its cdf by F(z).
47. 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.
Bias
covariance of X and Y
hypotheses
A likelihood function
48. Have no meaningful rank order among values.
Nominal measurements
Interval measurements
The average - or arithmetic mean
Inferential statistics
49. Is a parameter that indexes a family of probability distributions.
Dependent Selection
A random variable
Beta value
A Statistical parameter
50. ?
The Range
Simpson's Paradox
the population correlation
experimental studies and observational studies.