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| Section | Weight | Objectives |
|---|---|---|
| Basic Numeracy & Algebra | 15% | - Arithmetic operations, fractions, decimals, percentages - Linear equations, inequalities, graphing functions - Exponents, roots, and basic formulas |
| Inferential Statistics & Study Design | 20% | - Observational studies vs experiments - Sampling methods and bias - Hypothesis testing framework and interpretation - Confidence intervals for means/proportions |
| Descriptive Statistics | 25% | - Measures of center: mean, median, mode - Graphical displays: histograms, boxplots, scatterplots - Types of data: categorical, discrete, continuous - Measures of spread: range, IQR, variance, standard deviation |
| Correlation & Regression | 20% | - Interpreting slope, intercept, and R-squared - Predictions and limitations of regression - Correlation coefficient and interpretation - Simple linear regression models |
| Probability Concepts | 20% | - Conditional probability and Venn diagrams - Normal distribution and empirical rule - Discrete and continuous probability distributions - Probability rules, independent and dependent events |
>> Applied-Probability-and-Statistics學習筆記 <<
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問題 #76
Standard deviation increases #
答案：B
解題說明：
Standard deviation measures how far data values typically fall from the mean. When standard deviation increases, the data are more spread out. This means individual observations tend to be farther from the mean, producing greater variability. A smaller standard deviation means the data values are more tightly clustered around the mean. Option B states the opposite of the correct interpretation. Option C is incorrect because an increase in standard deviation does not necessarily mean the mean increases; center and spread are separate features of a distribution. Option D is also incorrect because variance is the square of standard deviation, so if standard deviation increases, variance increases as well, not decreases. Standard deviation is useful because it is expressed in the same units as the original data, making spread easier to interpret. Study Guide references
/topics: standard deviation, variance, spread, measures of variability.
問題 #77
Which distribution models number of successes in fixed independent trials?
答案：B
解題說明：
The binomial distribution models the number of successes in a fixed number of independent trials when each trial has only two possible outcomes, usually labeled success and failure, and the probability of success remains constant from trial to trial. These four conditions define the binomial setting: fixed number of trials, independent trials, two outcomes per trial, and constant success probability. Examples include the number of heads in 10 coin flips, the number of defective items in a sample when the defect probability is constant, or the number of students who pass an exam out of a fixed group. The normal distribution describes continuous bell-shaped data, not counts of successes. The Poisson distribution models counts of events occurring over a fixed interval when events occur at a constant average rate. The uniform distribution assigns equal probability across outcomes or intervals. Because the question explicitly states "number of successes" and "fixed independent trials," the correct model is binomial. Study Guide references/topics: binomial distribution, independent trials, success probability, discrete random variables.
問題 #78
Independent events: P(A|B) = ?
答案：B
解題說明：
For independent events, the occurrence of one event does not change the probability of the other. Conditional probability P(A|B) means the probability of A occurring given that B has occurred. If A and B are independent, knowing B occurred gives no new information about A. Therefore, P(A|B) = P(A). This is one of the defining properties of independence. For example, if a coin toss and a die roll are independent, knowing the die landed on 4 does not change the probability that the coin landed heads; it remains 1/2. Option B reverses the event being measured. Option C would imply that A becomes impossible after B, which describes a different situation. Option D is an addition expression and does not represent conditional probability. The correct relationship is that the conditional probability equals the original probability when events are independent. Study Guide references/topics: independent events, conditional probability, probability rules, event relationships.
問題 #79
Determine x:
4 + x = 6 # x
答案：A
解題說明：
The equation 4 + x = 6 # x is a linear equation in one variable. To solve it, collect variable terms on one side and constant terms on the other. Add x to both sides to eliminate the negative x on the right: 4 + 2x = 6. Then subtract 4 from both sides: 2x = 2. Finally, divide both sides by 2, giving x = 1. This value can be verified directly in the original equation. Substituting x = 1 gives 4 + 1 = 5 on the left and 6 # 1 = 5 on the right, so both sides are equal. Option A gives 4 = 6, which is false. Option C gives 6 = 4, also false. Option D gives 9 =
1, which is not valid. The correct solution is the value that balances both sides of the equation. References
/topics from the Study Guide: basic algebra, solving linear equations, inverse operations, substitution checks.
問題 #80
Correlation coefficient r = #0.9 indicates:
答案：C
解題說明：
The correlation coefficient r measures the direction and strength of a linear relationship between two quantitative variables. It ranges from #1 to 1. A value close to #1 indicates a strong negative linear relationship, meaning that as one variable increases, the other tends to decrease in a highly consistent linear pattern. Since r = #0.9 is very close to #1, the relationship is strong and negative. Option B is incorrect because the sign is negative, not positive. Option C identifies the direction correctly but understates the strength; #0.9 is not weak. Option D would correspond to r near 0, where there is little or no linear association. A scatterplot associated with r = #0.9 would show points clustered closely around a downward- sloping line. This does not prove causation; it describes linear association only. Study Guide references
/topics: correlation coefficient, negative association, strength of relationship, scatterplots.
問題 #81
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