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| Section | Weight | Objectives |
|---|---|---|
| Topic 1: Basic Numeracy & Algebra | 15% | - Arithmetic operations, fractions, decimals, percentages - Exponents, roots, and basic formulas - Linear equations, inequalities, graphing functions |
| Topic 2: Descriptive Statistics | 25% | - Types of data: categorical, discrete, continuous - Measures of center: mean, median, mode - Measures of spread: range, IQR, variance, standard deviation - Graphical displays: histograms, boxplots, scatterplots |
| Topic 3: Correlation & Regression | 20% | - Interpreting slope, intercept, and R-squared - Predictions and limitations of regression - Correlation coefficient and interpretation - Simple linear regression models |
| Topic 4: Probability Concepts | 20% | - Discrete and continuous probability distributions - Probability rules, independent and dependent events - Conditional probability and Venn diagrams - Normal distribution and empirical rule |
| Topic 5: Inferential Statistics & Study Design | 20% | - Sampling methods and bias - Confidence intervals for means/proportions - Hypothesis testing framework and interpretation - Observational studies vs experiments |
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NEW QUESTION # 17
Poisson used for:
Answer: D
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 # 18
If y = #4, evaluate the following expression:
(20 # y)/(5 + y)
Answer: B
Explanation:
To evaluate the expression, substitute y = #4 everywhere y appears. The numerator is 20 # y, so replacing y with #4 gives 20 # (#4). Subtracting a negative is equivalent to addition, so the numerator becomes 24. The denominator is 5 + y, so substituting #4 gives 5 + (#4) = 1. The expression therefore becomes 24/1, which equals 24. The correct answer is D. The most common error in this problem is mishandling the negative sign in the numerator. If a student incorrectly computes 20 # (#4) as 16, the resulting value would not match the correct algebraic structure. Another important check is that the denominator is not zero; here it equals 1, so the expression is defined. References/topics from the Study Guide: substitution, evaluating algebraic expressions, integers, order of operations.
NEW QUESTION # 19
t-test used when:
Answer: D
Explanation:
A t-test is used when making inferences about a population mean and the population standard deviation, #, is unknown. In practical settings, # is rarely available, so the sample standard deviation, s, is used as an estimate.
That substitution introduces additional uncertainty, which is why the t-distribution is used instead of the standard normal distribution. The t-distribution has heavier tails, especially for small samples, reflecting the extra variability caused by estimating # from the sample. Option B describes a z-test setting, where the population standard deviation is known. Option C is incorrect because categorical population data are usually analyzed with proportions, chi-square tests, or related categorical procedures, not mean-based t-tests. Option D is invalid because t-tests have a clear inferential role. The controlling condition is unknown #, with inference focused on means. Study Guide references/topics: t-tests, unknown population standard deviation, sample standard deviation, inferential statistics.
NEW QUESTION # 20
Best chart for categorical data?
Answer: A
Explanation:
A bar chart is the best display for categorical data because it shows the frequency or relative frequency of each category using separate bars. Categorical variables classify observations into groups, such as favorite color, type of transportation, political affiliation, or product category. A bar chart allows the viewer to compare category counts directly by bar height. A histogram is not appropriate because it is used for quantitative data grouped into numerical intervals. A scatterplot is used to examine the relationship between two quantitative variables, such as height and weight. A boxplot summarizes a quantitative distribution using quartiles, median, spread, and outliers. Since the question asks specifically about categorical data, the display must preserve category labels rather than numerical intervals or continuous measurement. Therefore, the bar chart is the correct choice. Study Guide references/topics: categorical data, bar charts, frequency displays, descriptive statistics.
NEW QUESTION # 21
Two dice rolled, probability of both even = ?
Answer: C
Explanation:
A standard six-sided die has three even outcomes: 2, 4, and 6. Thus, the probability that one die lands on an even number is 3/6 = 1/2. When two dice are rolled, the outcomes are independent because the result of one die does not affect the other. Therefore, the probability that both dice are even is 1/2 × 1/2 = 1/4.
Equivalently, there are 36 ordered outcomes for two dice. The even-even outcomes are formed from 3 even choices on the first die and 3 even choices on the second die, giving 3 × 3 = 9 favorable outcomes. Then 9/36 simplifies to 1/4. Option B gives the probability of one die being even, not both. Options C and D do not match the count or multiplication rule. Study Guide references/topics: independent events, dice probability, multiplication rule, sample space.
NEW QUESTION # 22
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