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| Section | Weight | Objectives |
|---|---|---|
| Inferential Statistics & Study Design | 20% | - Hypothesis testing framework and interpretation - Sampling methods and bias - Observational studies vs experiments - Confidence intervals for means/proportions |
| Descriptive Statistics | 25% | - Measures of spread: range, IQR, variance, standard deviation - Measures of center: mean, median, mode - Graphical displays: histograms, boxplots, scatterplots - Types of data: categorical, discrete, continuous |
| Probability Concepts | 20% | - Conditional probability and Venn diagrams - Probability rules, independent and dependent events - Normal distribution and empirical rule - Discrete and continuous probability distributions |
| Basic Numeracy & Algebra | 15% | - Arithmetic operations, fractions, decimals, percentages - Linear equations, inequalities, graphing functions - Exponents, roots, and basic formulas |
| Correlation & Regression | 20% | - Simple linear regression models - Correlation coefficient and interpretation - Interpreting slope, intercept, and R-squared - Predictions and limitations of regression |
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NEW QUESTION # 47
A t-distribution is used when:
Answer: B
Explanation:
A t-distribution is used for inference about a population mean when the population standard deviation # is unknown, especially with a small sample. In that situation, the sample standard deviation s must estimate #, creating extra uncertainty. The t-distribution accounts for this added uncertainty with heavier tails than the standard normal distribution. As sample size increases, the t-distribution becomes closer to the normal distribution. Option B describes a z-procedure setting, where # is known and the normal distribution may be used. Option C is incorrect because categorical data are usually analyzed with proportions or chi-square procedures, not t-distributions for means. Option D is incomplete: t-procedures typically require quantitative continuous or approximately continuous data, but the decisive condition in the answer set is unknown # with a small sample. Study Guide references/topics: t-distribution, unknown standard deviation, small samples, inference for means.
NEW QUESTION # 48
A biologist is studying the relationship between plant species, species A, species B, and species C, and the average height of the plants.
How should this study be classified?
Answer: B
Explanation:
This study compares two variables: plant species and average plant height. Plant species is categorical because it places each plant into a named group, such as species A, species B, or species C. These categories are labels rather than numerical measurements. Average height, however, is quantitative because it is measured numerically and can be compared using arithmetic operations such as differences, averages, and ranges. Since the explanatory or grouping variable is categorical and the measured outcome is quantitative, the relationship is classified as categorical-to-quantitative. This classification determines which statistical tools are appropriate. For example, side-by-side box plots, group means, or comparative summaries would be suitable because they compare numerical measurements across categories. A categorical-to-categorical study would involve two label-based variables, such as species and color group. A quantitative-to-quantitative study would involve two numerical variables, such as height and growth rate. References/topics from the Study Guide: two-variable data, categorical variables, quantitative variables, comparative statistical summaries.
NEW QUESTION # 49
Review the following inequality:
y < x # 1/2
Which shaded portion in the graphs corresponds to this inequality?



Answer: C
Explanation:
The inequality y < x # 1/2 has boundary line y = x # 1/2. This line has slope 1 and y-intercept #1/2, so it crosses the y-axis slightly below the origin and rises one unit for every one unit moved to the right. Because the inequality is strict, using " < " rather than "#," the boundary line must be dashed, showing that points on the line are not included in the solution set. The solution region must be shaded below the line because y is less than the expression x # 1/2. A useful verification method is the test point (0, 0). Substituting gives 0 < 0 #
1/2, or 0 < #1/2, which is false. Therefore, the region containing the origin should not be shaded. The fourth graph has the dashed boundary with intercept #1/2 and shades the region below the line while excluding the origin. References/topics from the Study Guide: graphing linear inequalities, slope-intercept form, dashed boundaries, test-point method.
NEW QUESTION # 50
Probability of at least one six in 2 dice rolls = ?
Answer: B
Explanation:
"At least one six" means one six or two sixes across the two rolls. The most efficient method is to use the complement rule. The complement of at least one six is no six on either roll. On one die roll, the probability of not rolling a six is 5/6. Since the two die rolls are independent, the probability of no six on both rolls is (5/6) (5/6) = 25/36. Therefore, the probability of at least one six is 1 # 25/36 = 11/36. This includes all outcomes with a six on the first roll, a six on the second roll, or sixes on both rolls. Option B gives the probability of a six on one single roll only. Option C gives the probability of rolling two sixes. Option D gives the complement, no sixes. Study Guide references/topics: complement rule, independent events, dice probability, sample spaces.
NEW QUESTION # 51
A golf course is attempting to correlate golfing handicap with math SAT scores among local high school golfers. Ignoring potential confounding variables such as socioeconomic status, the golf course creates the following scatterplot.
What is the estimated value of r, the correlation coefficient, between these variables?
Answer: A
Explanation:
The correlation coefficient r measures the direction and strength of a linear relationship between two quantitative variables. In the scatterplot, the points are widely dispersed, so the relationship is weak rather than strong. The fitted trend line slopes slightly downward, indicating a negative association: as golf handicap increases, math SAT score tends to decrease slightly. Because the pattern is weak and negative, r should be close to 0 but less than 0. The best match is #0.10. Option A, #0.63, would represent a moderately strong negative linear relationship, which would require the points to cluster more tightly around a downward- sloping line. Option C, 0.10, has the right weak magnitude but the wrong direction because it is positive.
Option D, 0.63, is both too strong and positive. The visual evidence supports only a very slight negative linear association. References/topics from the Study Guide: scatterplots, correlation coefficient, positive and negative association, strength of linear relationship.
NEW QUESTION # 52
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