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| Section | Weight | Objectives |
|---|---|---|
| Topic 1: Descriptive Statistics | 25% | - Measures of spread: range, IQR, variance, standard deviation - Graphical displays: histograms, boxplots, scatterplots - Measures of center: mean, median, mode - Types of data: categorical, discrete, continuous |
| Topic 2: Inferential Statistics & Study Design | 20% | - Sampling methods and bias - Hypothesis testing framework and interpretation - Observational studies vs experiments - Confidence intervals for means/proportions |
| Topic 3: Basic Numeracy & Algebra | 15% | - Linear equations, inequalities, graphing functions - Exponents, roots, and basic formulas - Arithmetic operations, fractions, decimals, percentages |
| Topic 4: Correlation & Regression | 20% | - Simple linear regression models - Interpreting slope, intercept, and R-squared - Predictions and limitations of regression - Correlation coefficient and interpretation |
| Topic 5: Probability Concepts | 20% | - Probability rules, independent and dependent events - Conditional probability and Venn diagrams - Normal distribution and empirical rule - Discrete and continuous probability distributions |
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質問 # 149
Expected value = ?
正解：A
解説：
Expected value is the theoretical long-term average outcome of a random variable over many repeated trials.
It is calculated by multiplying each possible value by its probability and then summing those products. For a discrete random variable, E(X) = #xP(x). Expected value does not necessarily have to be an outcome that can occur in one trial. For example, the expected value of rolling a fair six-sided die is 3.5, even though no face shows 3.5. It represents the balance point of the probability distribution. The median is the middle value of an ordered distribution, and the mode is the most likely or most frequent value. Expected value may equal 0 in some distributions, but it is not defined as 0. The best conceptual definition is long-term average. Study Guide references/topics: expected value, random variables, probability distributions, long-run average.
質問 # 150
Sum of probabilities in sample space = ?
正解：A
解説：
The probabilities of all outcomes in a complete sample space must sum to 1. A sample space contains every possible outcome of a probability experiment, and one of those outcomes must occur. For example, when rolling a fair six-sided die, the outcomes are 1, 2, 3, 4, 5, and 6. Each has probability 1/6, and the sum is 1/6 +
1/6 + 1/6 + 1/6 + 1/6 + 1/6 = 1. A total probability of 0 would mean no outcome can occur, which is impossible for a valid experiment. A total greater than 1 violates probability rules because probabilities cannot exceed certainty. "Cannot exceed 2" is too broad and mathematically invalid, since the exact total must equal
1. This principle is foundational for checking probability distributions and validating whether assigned probabilities are coherent. Study Guide references/topics: sample space, probability axioms, total probability, theoretical probability.
質問 # 151
A teacher plots the test scores of a class using the box plot.
What is true about the test scores?
正解：D
解説：
A box plot displays the five-number summary of a quantitative data set: minimum, first quartile, median, third quartile, and maximum. The median is represented by the vertical line inside the box. In the given box plot, that internal vertical line is positioned at 80 on the score axis. Therefore, the median test score for Class A is
80 points. The value 70 corresponds to the left edge of the box, which represents the first quartile, not the median. The value near 88 represents the right edge of the box, which is the third quartile. The whiskers extend to the approximate minimum and maximum scores, but those values do not determine the median. The median divides the ordered data into two equal halves, meaning about 50% of the students scored at or below
80 and about 50% scored at or above 80. References/topics from the Study Guide: box plots, five-number summary, median, quartiles.
質問 # 152
Probability it does NOT rain = 1 # 0.25 = ?
正解：B
解説：
This question uses the complement rule of probability. If the probability that it rains is 0.25, then the probability that it does not rain is the complement of that event. The complement rule states that P(not A) = 1
# P(A). Here, A represents the event "it rains," so P(not rain) = 1 # 0.25 = 0.75. This means there is a 75% probability that rain does not occur. Option B repeats the probability of rain rather than its complement.
Option C would imply rain and no rain are equally likely, which is not supported by the given probability.
Option D would mean no rain is certain, but a 0.25 probability of rain means rain is still possible. The key technical point is that an event and its complement must sum to 1. Study Guide references/topics: probability, complement rule, event probability, sample-space total.
質問 # 153
A fitness center owner notices that gym attendance increases as the number of daylight hours increases. The owner calculates a correlation coefficient between daylight hours and gym attendance of r = 0.72.
Based on this information, what can be concluded?
正解：B
解説：
The correlation coefficient r measures the direction and strength of a linear association between two quantitative variables. Since r = 0.72 is positive, the relationship is positive: as daylight hours increase, gym attendance tends to increase. The value 0.72 also indicates a moderately strong to strong linear association because it is closer to 1 than to 0. However, correlation alone does not establish causation. Even though daylight hours and gym attendance move together, other variables could influence attendance, such as weather, seasonal routines, work schedules, or fitness promotions. Therefore, the valid conclusion is that there is a positive association, not a proven causal relationship. Options A and B are incorrect because they describe a negative relationship, which conflicts with the positive correlation coefficient. Option D overstates the evidence by claiming causation. References/topics from the Study Guide: correlation coefficient, positive association, linear relationship, correlation versus causation.
質問 # 154
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