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CLEP General Mathematics: Probability And Statistics

Subjects : clep, 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. Is denoted by - pronounced 'x bar'.
A random variable
Probability
The arithmetic mean of a set of numbers x1 - x2 - ... - xn
Type I errors & Type II errors

2. 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}.
The sample space
A sampling distribution
the population variance
Simpson's Paradox

3. A collection of events is mutually independent if for any subset of the collection - the joint probability of all events occurring is equal to the product of the joint probabilities of the individual events. Think of the result of a series of coin-fl
The average - or arithmetic mean
Mutual independence
Seasonal effect
f(z) - and its cdf by F(z).

4. Statistics involve methods of organizing - picturing - and summarizing information from samples or population.
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
Probability density functions
Descriptive
Prior probability

5. Is the length of the smallest interval which contains all the data.
Probability density functions
The Range
categorical variables
Placebo effect

6. Failing to reject a false null hypothesis.
Beta value
Outlier
Parameter - or 'statistical parameter'
Type 2 Error

7. Gives the probability distribution for a continuous random variable.
A Distribution function
covariance of X and Y
Type I errors & Type II errors
A probability density function

8. Is one that explores the correlation between smoking and lung cancer. This type of study typically uses a survey to collect observations about the area of interest and then performs statistical analysis. In this case - the researchers would collect o
Observational study
Treatment
Coefficient of determination
Count data

9. Is the probability distribution - under repeated sampling of the population - of a given statistic.
A sampling distribution
Residuals
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.
Qualitative variable

10. E[X] :
expected value of X
Correlation coefficient
the sample or population mean
Count data

11. A scale that represents an ordinal scale such as looks on a scale from 1 to 10.
Likert scale
Confounded variables
Dependent Selection
Prior probability

12. A numerical measure that describes an aspect of a population.
quantitative variables
descriptive statistics
Parameter
Nominal measurements

13. Are usually written with upper case calligraphic (e.g. F for the set of sets on which we define the probability P)
s-algebras
Interval measurements
Valid measure
Atomic event

14. Is its expected value. The mean (or sample mean of a data set is just the average value.
Type II errors
The Mean of a random variable
Independent Selection
A random variable

15. When there is an even number of values...
That is the median value
experimental studies and observational studies.
Correlation
s-algebras

16. A list of individuals from which the sample is actually selected.
Qualitative variable
A random variable
That value is the median value
Sampling frame

17. 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
Sampling Distribution
Correlation
A sampling distribution
The average - or arithmetic mean

18. 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.
Treatment
Type II errors
hypothesis
Marginal probability

19. 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.
Step 3 of a statistical experiment
Type I errors
An experimental study
A Random vector

20. 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'
Statistical adjustment
the population correlation
A sample
Conditional probability

21. Rejecting a true null hypothesis.
Sample space
Greek letters
Type 1 Error
Independent Selection

22. The probability distribution of a sample statistic based on all the possible simple random samples of the same size from a population.
Binomial experiment
Correlation coefficient
Sampling Distribution
Probability density functions

23. Is data arising from counting that can take only non-negative integer values.
That value is the median value
Count data
Random variables
The standard deviation

24. 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.
Quantitative variable
That value is the median value
inferential statistics
A random variable

25. Are usually written in upper case roman letters: X - Y - etc.
Sampling frame
the sample or population mean
A Statistical parameter
Random variables

26. S^2
Parameter
Inferential
Divide the sum by the number of values.
the population variance

27. Is a function of the known data that is used to estimate an unknown parameter; an estimate is the result from the actual application of the function to a particular set of data. The mean can be used as an estimator.
Estimator
Random variables
Statistical inference
Power of a test

28. Is data that can take only two values - usually represented by 0 and 1.
Binary data
Probability density
Quantitative variable
covariance of X and Y

29. In particular - the pdf of the standard normal distribution is denoted by
Null hypothesis
Divide the sum by the number of values.
Type II errors
f(z) - and its cdf by F(z).

30. 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.
Treatment
Correlation
The median value
Dependent Selection

31. A variable describes an individual by placing the individual into a category or a group.
Inferential
Standard error
Statistical inference
Qualitative variable

32. 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.
Correlation
Descriptive statistics
A Distribution function
hypothesis

33. ?
Standard error
the sample or population mean
the population correlation
Inferential statistics

34. Two variables such that their effects on the response variable cannot be distinguished from each other.
Simple random sample
Individual
A random variable
Confounded variables

35. Another name for elementary event.
Descriptive statistics
Outlier
the population mean
Atomic event

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.

37. 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).
That is the median value
Step 1 of a statistical experiment
An event
Mutual independence

38. Is that part of a population which is actually observed.
That is the median value
The Mean of a random variable
A sample
methods of least squares

39. Used to reduce bias - this measure weights the more relevant information higher than less relevant info.
Statistical adjustment
Variability
A probability space
Probability density functions

40. Some commonly used symbols for sample statistics
Coefficient of determination
hypothesis
Binomial experiment
the sample mean - the sample variance s2 - the sample correlation coefficient r - the sample cumulants kr.

41. 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
inferential statistics
Qualitative variable
Correlation coefficient
expected value of X

42. Statistical methods can be used for summarizing or describing a collection of data; this is called
Nominal measurements
Likert scale
descriptive statistics
covariance of X and Y

43. A numerical facsimilie or representation of a real-world phenomenon.
Skewness
A Random vector
Simulation
Type 1 Error

44. Consists of a number of independent trials repeated under identical conditions. On each trial - there are two possible outcomes.
Coefficient of determination
A Distribution function
Binomial experiment
Sampling Distribution

45. A variable has a value or numerical measurement for which operations such as addition or averaging make sense.
Qualitative variable
Quantitative variable
The Covariance between two random variables X and Y - with expected values E(X) =
Nominal measurements

46. Have imprecise differences between consecutive values - but have a meaningful order to those values
Ordinal measurements
the sample or population mean
A Probability measure
hypotheses

47. (or multivariate random variable) is a vector whose components are random variables on the same probability space.
Step 1 of a statistical experiment
Variability
A Random vector
Residuals

48. 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
A probability distribution
Parameter
Type 1 Error
experimental studies and observational studies.

49. The probability of the observed value or something more extreme under the assumption that the null hypothesis is true.
An estimate of a parameter
P-value
the population mean
Reliable measure

50. Ratio and interval measurements which can be either discrete or continuous - due to their numerical nature are grouped together as
A probability distribution
quantitative variables
the population mean
The Expected value