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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
study here
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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. 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
A probability distribution
Skewness
Sampling frame
Correlation
2. 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
P-value
An estimate of a parameter
Probability
Step 3 of a statistical experiment
3. (cdfs) are denoted by upper case letters - e.g. F(x).
Confounded variables
Descriptive
Cumulative distribution functions
A data point
4. Another name for elementary event.
Atomic event
Step 1 of a statistical experiment
A likelihood function
Inferential
5. Is inference about a population from a random sample drawn from it or - more generally - about a random process from its observed behavior during a finite period of time.
Treatment
Random variables
Residuals
Statistical inference
6. Consists of a number of independent trials repeated under identical conditions. On each trial - there are two possible outcomes.
Atomic event
Statistic
Binomial experiment
Power of a test
7. Two events are independent if the outcome of one does not affect that of the other (for example - getting a 1 on one die roll does not affect the probability of getting a 1 on a second roll). Similarly - when we assert that two random variables are i
Independence or Statistical independence
A sample
Count data
Treatment
8. When you have two or more competing models - choose the simpler of the two models.
Count data
Law of Parsimony
the population mean
Greek letters
9. 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
Atomic event
Skewness
Joint probability
A random variable
10. The objects described by a set of data: person (animal) - place - and - thing. (SUBJECTS)
Beta value
Quantitative variable
Individual
A probability density function
11. 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.
the population mean
Kurtosis
Inferential
Cumulative distribution functions
12. Statistical methods can be used for summarizing or describing a collection of data; this is called
Type I errors & Type II errors
descriptive statistics
Correlation
Individual
13. 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
Independence or Statistical independence
Descriptive statistics
Prior probability
14. 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.
Seasonal effect
Marginal distribution
Treatment
Type 2 Error
15. A consistent - repeated deviation of the sample statistic from the population parameter in the same direction when many samples are taken.
Bias
The variance of a random variable
Interval measurements
Block
16. Where the null hypothesis fails to be rejected and an actual difference between populations is missed giving a 'false negative'.
The Mean of a random variable
Type II errors
Statistical inference
Valid measure
17. 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
Outlier
descriptive statistics
A likelihood function
18. Probability of rejecting a true null hypothesis.
Binary data
P-value
Alpha value (Level of Significance)
Inferential statistics
19. A common goal for a statistical research project is to investigate causality - and in particular to draw a conclusion on the effect of changes in the values of predictors or independent variables on dependent variables or response.
Variable
P-value
Experimental and observational studies
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
20. Any specific experimental condition applied to the subjects
Residuals
nominal - ordinal - interval - and ratio
Treatment
Type I errors & Type II errors
21. (or multivariate random variable) is a vector whose components are random variables on the same probability space.
Cumulative distribution functions
Statistics
methods of least squares
A Random vector
22. Is the probability of some event A - assuming event B. Conditional probability is written P(A|B) - and is read 'the probability of A - given B'
Skewness
The sample space
Conditional probability
Sampling frame
23. ?
Descriptive statistics
Beta value
the population correlation
Bias
24. Gives the probability distribution for a continuous random variable.
Ordinal measurements
The median value
A probability density function
Probability and statistics
25. (also called statistical variability) is a measure of how diverse some data is. It can be expressed by the variance or the standard deviation.
Outlier
Greek letters
Statistical dispersion
The average - or arithmetic mean
26. A measurement such that the random error is small
Reliable measure
A Random vector
Probability and statistics
Marginal distribution
27. Is the probability distribution - under repeated sampling of the population - of a given statistic.
Credence
That value is the median value
A sampling distribution
Mutual independence
28. E[X] :
Mutual independence
Law of Parsimony
Kurtosis
expected value of X
29. 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 probability distribution
Joint probability
Step 2 of a statistical experiment
Statistics
30. The standard deviation of a sampling distribution.
Standard error
The Expected value
Correlation coefficient
Independent Selection
31. Long-term upward or downward movement over time.
Inferential statistics
experimental studies and observational studies.
Trend
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
32. (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
Probability and statistics
That value is the median value
Observational study
The Expected value
33. 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.
Statistical inference
Count data
Experimental and observational studies
Simple random sample
34. A numerical measure that assesses the strength of a linear relationship between two variables.
Step 1 of a statistical experiment
Nominal measurements
Correlation coefficient
A statistic
35. When info. in a contingency table is re-organized into more or less categories - relationships seen can change or reverse.
36. 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.
the population mean
Conditional distribution
Type I errors & Type II errors
Interval measurements
37. Working from a null hypothesis two basic forms of error are recognized:
Type I errors & Type II errors
Outlier
Block
Statistic
38. 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.
39. Are usually written with upper case calligraphic (e.g. F for the set of sets on which we define the probability P)
s-algebras
observational study
Marginal distribution
The average - or arithmetic mean
40. 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)
Posterior probability
Power of a test
Interval measurements
Parameter - or 'statistical parameter'
41. 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
Estimator
Correlation coefficient
Ratio measurements
Divide the sum by the number of values.
42. 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.
Treatment
Joint probability
An experimental study
Greek letters
43. 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 population mean
the population variance
Observational study
A population or statistical population
44. (e.g. ? - b) are commonly used to denote unknown parameters (population parameters).
Law of Large Numbers
Greek letters
Step 3 of a statistical experiment
Random variables
45. Rejecting a true null hypothesis.
Type 1 Error
A probability density function
A sample
Alpha value (Level of Significance)
46. Is its expected value. The mean (or sample mean of a data set is just the average value.
The Mean of a random variable
Correlation
Probability
s-algebras
47. 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.
nominal - ordinal - interval - and ratio
A sampling distribution
Confounded variables
Independent Selection
48. Is data that can take only two values - usually represented by 0 and 1.
Law of Parsimony
Sample space
Particular realizations of a random variable
Binary data
49. Is a sample space over which a probability measure has been defined.
the population mean
Independence or Statistical independence
A probability space
Correlation coefficient
50. Because variables conforming only to nominal or ordinal measurements cannot be reasonably measured numerically - sometimes they are grouped together as
categorical variables
A Probability measure
The median value
Outlier