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| Section | Weight | Objectives |
|---|---|---|
| Correlation & Regression | 20% | - Interpreting slope, intercept, and R-squared - Predictions and limitations of regression - Simple linear regression models - Correlation coefficient and interpretation |
| 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 |
| 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% | - Arithmetic operations, fractions, decimals, percentages - Linear equations, inequalities, graphing functions - Exponents, roots, and basic formulas |
| Probability Concepts | 20% | - Conditional probability and Venn diagrams - Discrete and continuous probability distributions - Probability rules, independent and dependent events - Normal distribution and empirical rule |
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NEW QUESTION # 47
Probability of drawing red or black card = ?
Answer: B
Explanation:
In a standard deck of playing cards, every card is either red or black. Red cards consist of hearts and diamonds, and black cards consist of clubs and spades. There are 26 red cards and 26 black cards, for a total of 52 cards. The event "red or black" includes all possible cards in the deck. Therefore, the probability is 52 favorable outcomes out of 52 total outcomes, which equals 1. A probability of 1 means the event is certain.
Option B, 1/2, would be the probability of drawing a red card alone or a black card alone, not red or black.
Option C would mean the event is impossible, which is false. Option D would correspond to one suit out of four, such as hearts only. The word "or" combines both color categories, covering the entire sample space.
Study Guide references/topics: sample space, certainty, addition rule, card probability.
NEW QUESTION # 48
Two events mutually exclusive # P(A and B) = ?
Answer: D
Explanation:
Mutually exclusive events cannot happen at the same time. Therefore, the probability of their intersection is zero: P(A and B) = 0. For instance, on a single coin toss, the event "heads" and the event "tails" are mutually exclusive because a single toss cannot produce both outcomes. Option B applies to independent events when calculating the probability of both occurring, but mutually exclusive events with positive probabilities are not independent because one event prevents the other from occurring. Option C is used to find P(A or B) for mutually exclusive events, not P(A and B). Option D would mean both events always occur together, which directly contradicts mutual exclusivity. The word "and" is the key operator: it asks for overlap. Since mutually exclusive events have no overlap, the result is 0. Study Guide references/topics: mutually exclusive events, intersections, joint probability, addition rule.
NEW QUESTION # 49
Poisson used for:
Answer: A
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 # 50
Sample mean = 40, SD = 8, n = 16. Standard error = ?
Answer: D
Explanation:
The standard error of the sample mean is calculated as SE = s/#n, where s is the sample standard deviation and n is the sample size. Here, the standard deviation is 8 and the sample size is 16. The square root of 16 is 4, so SE = 8/4 = 2. The sample mean of 40 is not used directly in the standard error formula; it identifies the center of the sample, not the variability of the sample mean across repeated samples. Option B, 8, is the standard deviation, not the standard error. Option D, 4, is the square root of the sample size. Option C, 0.5, would result from an incorrect calculation. Standard error decreases as sample size increases because larger samples provide more precise estimates. Study Guide references/topics: standard error, standard deviation, sample size, sampling distribution.
NEW QUESTION # 51
Determine x:
4 + x = 6 # x
Answer: B
Explanation:
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.
NEW QUESTION # 52
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