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| Section | Weight | Objectives |
|---|---|---|
| Correlation & Regression | 20% | - Correlation coefficient and interpretation - Simple linear regression models - Interpreting slope, intercept, and R-squared - Predictions and limitations of regression |
| Basic Numeracy & Algebra | 15% | - Exponents, roots, and basic formulas - Arithmetic operations, fractions, decimals, percentages - Linear equations, inequalities, graphing functions |
| Probability Concepts | 20% | - Discrete and continuous probability distributions - Conditional probability and Venn diagrams - Normal distribution and empirical rule - Probability rules, independent and dependent events |
| Descriptive Statistics | 25% | - Measures of spread: range, IQR, variance, standard deviation - Graphical displays: histograms, boxplots, scatterplots - Types of data: categorical, discrete, continuous - Measures of center: mean, median, mode |
| Inferential Statistics & Study Design | 20% | - Confidence intervals for means/proportions - Hypothesis testing framework and interpretation - Sampling methods and bias - Observational studies vs experiments |
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NEW QUESTION # 50
A hospital analyzes the recovery rates of patients undergoing two different treatments for a specific condition.
Treatment X has an overall recovery rate of 80%, while Treatment Y has a recovery rate of 90%. However, when the data is divided by age groups, Treatment X has a higher recovery rate in each age group compared to Treatment Y.
Is Simpson's paradox present in this study?
Answer: B
Explanation:
Simpson's paradox occurs when an association observed in aggregated data reverses or conflicts with the association observed within relevant subgroups. In this case, the overall recovery rate appears better for Treatment Y, since Y has a 90% overall recovery rate compared with 80% for Treatment X. However, after the data are divided by age group, Treatment X has a higher recovery rate in every age group. That reversal between the overall comparison and the subgroup comparisons is precisely the defining structure of Simpson' s paradox. Age group functions as the lurking or confounding variable because different age distributions across treatment groups can distort the overall recovery rates. Option B states a true overall fact, but it ignores the contradiction created by the age-specific rates. Option C is too general; simple differences between treatments do not necessarily create Simpson's paradox. The key issue is inconsistency between aggregate and stratified results. References/topics from the Study Guide: two-variable data, confounding variables, conditional comparisons, Simpson's paradox.
NEW QUESTION # 51
Probability it does NOT rain = 1 # 0.25 = ?
Answer: C
NEW QUESTION # 52
Binomial expected value = ?
Answer: A
Explanation:
For a binomial random variable, the expected value is E(X) = np, where n is the number of trials and p is the probability of success on each trial. The binomial model applies when there is a fixed number of independent trials, each trial has two outcomes, and the probability of success remains constant. The expected value represents the long-run average number of successes across repeated binomial experiments. For example, if a test has 20 independent questions and the probability of success on each is 0.75, the expected number correct is 20 × 0.75 = 15. Option B, n/p, and option C, p/n, do not represent the binomial mean. Option D, n + p, incorrectly adds the number of trials and success probability, which are not comparable units. The formula np captures both how many opportunities there are and how likely success is on each opportunity. Study Guide references/topics: binomial distribution, expected value, success probability, discrete random variables.
NEW QUESTION # 53
Poisson used for:
Answer: B
Explanation:
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.
NEW QUESTION # 54
Conditional probability formula:
Answer: C
Explanation:
Conditional probability measures the probability that event A occurs given that event B has already occurred.
The formula is P(A|B) = P(A and B)/P(B), assuming P(B) is greater than zero. The denominator P(B) restricts the sample space to cases where B occurs, and the numerator P(A and B) counts cases where both A and B occur within that restricted space. Option B is incorrect because it divides P(A) by P(B) without requiring overlap between A and B. Option C reverses the conditioning and would relate to P(B|A) only if the numerator were P(A and B). Option D applies to independent events when finding P(A and B), not to conditional probability in general. The vertical bar in P(A|B) is read as "given," and it signals that the denominator should be the probability of the given event. Study Guide references/topics: conditional probability, joint probability, event intersection, probability rules.
NEW QUESTION # 55
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