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| Section | Weight | Objectives |
|---|---|---|
| Inferential Statistics & Study Design | 20% | - Observational studies vs experiments - Confidence intervals for means/proportions - Sampling methods and bias - Hypothesis testing framework and interpretation |
| Correlation & Regression | 20% | - Correlation coefficient and interpretation - Simple linear regression models - Predictions and limitations of regression - Interpreting slope, intercept, and R-squared |
| Basic Numeracy & Algebra | 15% | - Exponents, roots, and basic formulas - Linear equations, inequalities, graphing functions - Arithmetic operations, fractions, decimals, percentages |
| Descriptive Statistics | 25% | - Measures of spread: range, IQR, variance, standard deviation - Measures of center: mean, median, mode - Types of data: categorical, discrete, continuous - Graphical displays: histograms, boxplots, scatterplots |
| Probability Concepts | 20% | - Conditional probability and Venn diagrams - Probability rules, independent and dependent events - Normal distribution and empirical rule - Discrete and continuous probability distributions |
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NEW QUESTION # 128
Mean = 50, SD = 5, n = 25. Standard error = ?
Answer: C
Explanation:
The standard error of the mean measures the expected sampling variability of the sample mean. It is calculated by dividing the sample standard deviation by the square root of the sample size: SE = s / #n. In this question, the standard deviation is 5 and the sample size is 25. Therefore, SE = 5 / #25 = 5 / 5 = 1. The mean of 50 identifies the center of the sample distribution but is not directly used in the standard error calculation.
Option B, 5, is the standard deviation, not the standard error. Option C, 25, is the sample size. Option D, 0.2, would result from incorrectly dividing 5 by 25 rather than by the square root of 25. The distinction between standard deviation and standard error is important: standard deviation describes spread among individual observations, while standard error describes spread among sample means. Study Guide references/topics:
standard error, standard deviation, sample size, sampling distributions.
NEW QUESTION # 129
A single ball is drawn from an opaque bag that contains red, blue, and green balls. The probability of drawing a red ball is .3, and the probability of drawing a blue ball is .6.
What is the probability of drawing a green ball?
Answer: A
Explanation:
The probabilities of all possible outcomes in a sample space must sum to 1. In this experiment, the bag contains only red, blue, and green balls, so these three outcomes exhaust the sample space. The probability of drawing a red ball is 0.3, and the probability of drawing a blue ball is 0.6. Their combined probability is 0.3 +
0.6 = 0.9. The remaining probability must belong to drawing a green ball. Therefore, P(green) = 1 # 0.9 = 0.1.
This can also be viewed as a complement problem: green is the complement of drawing either red or blue when those are the only other colors available. Option B repeats the red probability, option C would make the total probability exceed 1, and option D is the combined probability of red or blue rather than green.
References/topics from the Study Guide: probability sum rule, complements, sample space, mutually exclusive outcomes.
NEW QUESTION # 130
Review the following inequality:
y < x # 1/2
Which shaded portion in the graphs corresponds to this inequality?
Answer: B
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 # 131
There are 20 men in a room whose heights are reflected in inches as 68, 70, 73, 67, 71, 68, 76, 70, 73, 66, 68,
69, 71, 74, 73, 72, 65, 60, 70, and 78 inches respectively.
What is the median of these data?
Answer: A
Explanation:
The median is the middle value of an ordered data set. Because there are 20 observations, the number of data values is even, so the median is the average of the 10th and 11th values after the data are arranged from least to greatest. Ordering the heights gives 60, 65, 66, 67, 68, 68, 68, 69, 70, 70, 70, 71, 71, 72, 73, 73, 73, 74, 76,
78. The 10th value is 70, and the 11th value is also 70. The median is therefore (70 + 70) ÷ 2 = 70. This value divides the ordered heights into two equal halves: ten values are at or below 70, and ten values are at or above
70. The median is resistant to extreme values, so the low value 60 and the high value 78 do not distort it the way they could affect the mean. References/topics from the Study Guide: median, ordered data, measures of center, quantitative data.
NEW QUESTION # 132
R² = 0.81 # correlation r = ?
Answer: D
Explanation:
In simple linear regression, R² is the square of the correlation coefficient r. Therefore, to recover the possible correlation value from R², take the square root: r = ±#R². With R² = 0.81, the square root is #0.81 = 0.9, so r may be +0.9 or #0.9. The sign cannot be determined from R² alone because squaring removes direction. A positive r would indicate an upward linear association, while a negative r would indicate a downward linear association. Option D gives only +0.9, which would be correct only if the slope or scatterplot confirmed a positive relationship. Option B incorrectly treats R² as though it were r. Option C incorrectly keeps 0.81 after applying the square-root relationship. The technically complete answer is ±0.9. Study Guide references
/topics: coefficient of determination, correlation coefficient, regression, explained variation.
NEW QUESTION # 133
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