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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 |
| Probability Concepts | 20% | - Discrete and continuous probability distributions - Conditional probability and Venn diagrams - Normal distribution and empirical rule - Probability rules, independent and dependent events |
| Correlation & Regression | 20% | - Simple linear regression models - Predictions and limitations of regression - Interpreting slope, intercept, and R-squared - Correlation coefficient and interpretation |
| Inferential Statistics & Study Design | 20% | - Confidence intervals for means/proportions - Sampling methods and bias - Observational studies vs experiments - Hypothesis testing framework and interpretation |
| Basic Numeracy & Algebra | 15% | - Exponents, roots, and basic formulas - Arithmetic operations, fractions, decimals, percentages - Linear equations, inequalities, graphing functions |
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NEW QUESTION # 71
What is true about the correlation between the variables?
Answer: C
Explanation:
The scatterplot shows a clear downward pattern: as x increases, y tends to decrease. This establishes a negative correlation. The strength of a correlation is judged by how closely the points follow a general linear pattern. Here, although the points are not perfectly aligned, they form a visible descending band from upper left to lower right. That pattern is much stronger than a weak association, where the points would appear widely scattered with only a slight trend. Therefore, the best description is a strong negative correlation.
Options C and D are incorrect because they describe positive correlation, which would require y to increase as x increases. Option A correctly identifies the negative direction but understates the strength of the pattern. In correlation terminology, a strong negative value would have r substantially below 0 and closer to #1 than to 0.
References/topics from the Study Guide: scatterplots, negative correlation, correlation strength, bivariate quantitative data.
NEW QUESTION # 72
There are 14 black, 16 white, and 10 red balls in a box.
What is the probability of selecting 1 black ball, then 1 red ball, and then 1 white ball, replacing the ball each time?
Answer: B
Explanation:
The box contains 14 black, 16 white, and 10 red balls, for a total of 40 balls. Because the ball is replaced after each selection, the probability of each color remains constant on every draw. This makes the three draws independent. The probability of selecting a black ball first is 14/40, which simplifies to 7/20. The probability of selecting a red ball second is 10/40, or 1/4. The probability of selecting a white ball third is 16/40, or 2/5.
Since the question asks for all three events in the stated order, multiply the probabilities: (7/20)(1/4)(2/5) = 14
/400 = 7/200. Replacement is the controlling condition; without replacement, the denominators would decrease after each draw. Here, the sample space remains 40 each time. References/topics from the Study Guide: probability, independent events, replacement, multiplication rule.
NEW QUESTION # 73
Probability of rolling sum = 12 = ?
Answer: D
Explanation:
Rolling two six-sided dice produces 36 equally likely ordered outcomes. A sum of 12 can occur only when both dice show 6, giving the single ordered pair (6, 6). Since there is exactly 1 favorable outcome out of 36 total outcomes, the probability is 1/36. This is structurally similar to rolling a sum of 2, where only (1, 1) works. Option B, 1/6, is much too large and would apply to one specified face on one die. Option C, 2/36, would require two different ordered outcomes, but no pair other than (6, 6) sums to 12. Option D, 1/12, also overstates the probability. Extreme sums such as 2 and 12 are least likely because they have only one possible ordered combination. Study Guide references/topics: sample spaces, dice sums, theoretical probability, equally likely outcomes.
NEW QUESTION # 74
What is the mode of this dataset: 3, 5, 7, 7, 10?
Answer: B
Explanation:
The mode is the value that occurs most frequently in a data set. In the set 3, 5, 7, 7, 10, the value 3 appears once, 5 appears once, 10 appears once, and 7 appears twice. Since 7 has the highest frequency, it is the mode.
This question tests recognition of a measure of center that differs from the mean and median. The mean would require summing all values and dividing by the number of observations, while the median would identify the middle value after ordering the data. The data are already ordered, and the middle value is also 7, but the reason the correct answer is 7 here is specifically because it appears more often than any other value. Options A, B, and D each name values that occur only once, so none can be the mode. A dataset may have one mode, multiple modes, or no mode, but this dataset is unimodal. References/topics from the Study Guide: descriptive statistics, measures of center, frequency, mode.
NEW QUESTION # 75
A school surveyed student participation in extracurricular activities. The survey found:
* The drama club had 50% of students participate.
* The science club had 30% of students participate.
* Both clubs had 15% of students participate.
What is the probability that a student participated in the drama club, given that they attended the science club?
Answer: C
Explanation:
This question asks for a conditional probability. The phrase "given that they attended the science club" means the science club group becomes the restricted reference group. The required probability is P(drama club | science club), which is calculated as P(drama and science) divided by P(science). The problem states that 15% of students participated in both clubs, so P(drama and science) = 0.15. It also states that 30% participated in the science club, so P(science) = 0.30. Therefore, P(drama | science) = 0.15 ÷ 0.30 = 0.50. This means that among students who attended the science club, half also participated in drama club. Option A gives the joint probability, not the conditional probability. Option B gives only the science club participation rate. Option C does not match the conditional probability calculation. References/topics from the Study Guide: conditional probability, joint probability, probability ratios, two-event probability.
NEW QUESTION # 76
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