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| Section | Weight | Objectives |
|---|---|---|
| Descriptive Statistics | 25% | - Measures of center: mean, median, mode - Graphical displays: histograms, boxplots, scatterplots - Measures of spread: range, IQR, variance, standard deviation - Types of data: categorical, discrete, continuous |
| Basic Numeracy & Algebra | 15% | - Exponents, roots, and basic formulas - Arithmetic operations, fractions, decimals, percentages - Linear equations, inequalities, graphing functions |
| Correlation & Regression | 20% | - Interpreting slope, intercept, and R-squared - Simple linear regression models - Predictions and limitations of regression - Correlation coefficient and interpretation |
| Probability Concepts | 20% | - Conditional probability and Venn diagrams - Probability rules, independent and dependent events - Normal distribution and empirical rule - Discrete and continuous probability distributions |
| Inferential Statistics & Study Design | 20% | - Sampling methods and bias - Observational studies vs experiments - Hypothesis testing framework and interpretation - Confidence intervals for means/proportions |
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31. Frage
Mean of Poisson # = 5 = ?
Antwort: C
Begründung:
For a Poisson distribution, the parameter # represents the mean number of events occurring in a fixed interval.
Therefore, if # = 5, the mean is 5. This means that over many repeated intervals of the same size, the long-run average number of events per interval would be 5. The Poisson distribution is used for count data, such as calls per hour, accidents per week, or defects per batch, when events occur independently and at a constant average rate. A special property of the Poisson distribution is that its variance also equals #, so in this case the variance would also be 5. However, the question asks for the mean, so the direct answer is 5. Options B, C, and D are not supported by the stated parameter. Study Guide references/topics: Poisson distribution, # parameter, expected value, count data.
32. Frage
Poisson used for:
Antwort: C
Begründung:
The Poisson distribution is used to model counts of events occurring within a fixed interval of time, space, area, or volume, especially when the events are relatively rare and occur at a constant average rate. Examples include the number of calls received per hour, accidents per month, defects per batch, or arrivals at a service counter per minute. Its parameter # represents the average number of events per interval. Option B describes the binomial distribution, which models the number of successes in a fixed number of independent success
/failure trials. Option C is incorrect because Poisson outcomes are discrete counts, not continuous measurements. Option D is also incorrect because categorical data classify observations into groups, while Poisson data count event occurrences. The phrase "rare events per interval" is the defining clue for the Poisson model. Study Guide references/topics: Poisson distribution, rare-event counts, # parameter, discrete probability models.
33. Frage
Confidence interval = sample mean ± ?
Antwort: B
Begründung:
A confidence interval for a population mean is generally constructed as sample mean ± margin of error. The margin of error equals a critical value multiplied by the standard error. Therefore, the structure is sample mean ± critical value × SE. The critical value depends on the confidence level and distribution used, such as a z critical value when the population standard deviation is known or a t critical value when it is unknown. The standard error measures the sampling variability of the sample mean, often computed as s/#n when using sample standard deviation. Option B is incorrect because variance times sample size is not a margin of error.
Option C is incomplete because standard deviation alone measures spread among data values, not uncertainty of the sample mean. Option D is incorrect because the median is a measure of center and is not the typical component of a mean-based confidence interval. Study Guide references/topics: confidence intervals, standard error, critical value, margin of error.
34. Frage
Conditional probability P(A|B) = P(A and B)/P(B) #
Antwort: D
Begründung:
The formula for conditional probability is P(A|B) = P(A and B)/P(B), provided P(B) > 0. The notation P(A|B) is read as "the probability of A given B." The denominator P(B) restricts the sample space to cases in which B occurs, and the numerator P(A and B) counts the portion of that restricted group in which A also occurs.
Therefore, the statement is true. Option B is incorrect because the formula is the standard definition of conditional probability. Option C is incorrect because if A and B are mutually exclusive, then P(A and B) = 0, which creates a special case rather than the general definition. Option D is invalid because conditional probability is undefined when P(B) = 0. The condition must have positive probability. Study Guide references
/topics: conditional probability, joint probability, event intersection, probability rules.
35. Frage
Standard deviation measures:
Antwort: B
Begründung:
Standard deviation measures how spread out data values are around the mean. A smaller standard deviation indicates that values are clustered closely near the mean, while a larger standard deviation indicates greater variability. Standard deviation is based on deviations from the mean, squared deviations, variance, and then the square root of variance. It is expressed in the original units of measurement, making it easier to interpret than variance. Option B is incorrect because central tendency is measured by statistics such as the mean, median, and mode. Option C is incorrect because probability measures likelihood, not data dispersion. Option D refers to frequency or the number of observations, not their variability. For example, two classes could have the same mean test score but different standard deviations; the class with the larger standard deviation has more varied scores. Study Guide references/topics: standard deviation, variance, spread, descriptive statistics.
36. Frage
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