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| Section | Weight | Objectives |
|---|---|---|
| Topic 1: Correlation & Regression | 20% | - Predictions and limitations of regression - Correlation coefficient and interpretation - Interpreting slope, intercept, and R-squared - Simple linear regression models |
| Topic 2: Probability Concepts | 20% | - Normal distribution and empirical rule - Conditional probability and Venn diagrams - Probability rules, independent and dependent events - Discrete and continuous probability distributions |
| Topic 3: Inferential Statistics & Study Design | 20% | - Confidence intervals for means/proportions - Sampling methods and bias - Observational studies vs experiments - Hypothesis testing framework and interpretation |
| Topic 4: Basic Numeracy & Algebra | 15% | - Exponents, roots, and basic formulas - Arithmetic operations, fractions, decimals, percentages - Linear equations, inequalities, graphing functions |
| Topic 5: Descriptive Statistics | 25% | - Measures of spread: range, IQR, variance, standard deviation - Graphical displays: histograms, boxplots, scatterplots - Measures of center: mean, median, mode - Types of data: categorical, discrete, continuous |
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NEW QUESTION # 108
Probability of rolling 1, 2, or 3 on die = ?
Answer: A
Explanation:
A standard six-sided die has six equally likely outcomes: 1, 2, 3, 4, 5, and 6. The event "rolling 1, 2, or 3" has three favorable outcomes: 1, 2, and 3. The probability is therefore favorable outcomes divided by total outcomes: 3/6. This fraction simplifies to 1/2. Option B, 1/3, would correspond to two favorable outcomes out of six. Option C, 1/6, is the probability of rolling one specific number only. Option D, 2/3, would require four favorable outcomes out of six. Since exactly half of the die faces are 1, 2, or 3, the correct probability is one- half. This is a direct application of theoretical probability with equally likely outcomes. Study Guide references/topics: die probability, favorable outcomes, sample space, theoretical probability.
NEW QUESTION # 109
Uniform distribution 0-5: P(X < 3) = ?
Answer: B
Explanation:
For a continuous uniform distribution on the interval from 0 to 5, probability is proportional to interval length.
The total interval length is 5 # 0 = 5. The event X < 3 corresponds to the interval from 0 to 3, which has length 3. Therefore, P(X < 3) = 3/5 = 0.6. This works because the uniform distribution assigns constant density across the entire interval, so any subinterval's probability equals its length divided by the total length.
Option B would correspond to half the interval, such as X < 2.5. Option C would correspond to length 2 out of
5. Option D incorrectly treats the cutoff value 3 as if it were a percentage rather than an interval boundary.
The correct answer is 0.6, meaning 60% of the uniform distribution lies below 3. Study Guide references
/topics: uniform distribution, continuous probability, interval length, probability density.
NEW QUESTION # 110
In hypothesis testing, rejecting H# when true = ?
Answer: A
Explanation:
A Type I error occurs when the null hypothesis, H#, is true but the test decision rejects it. In plain statistical language, this is a false positive: the analysis concludes that there is evidence of an effect, difference, or relationship when in reality the null condition is true. The probability of making a Type I error is denoted by
#, the significance level, commonly set at 0.05. A Type II error is different; it occurs when the null hypothesis is false but the test fails to reject it. That is a false negative. Option C is incorrect because rejecting a true null is not a correct decision. Option D describes not rejecting or accepting the null, not the stated event. The critical phrase is "rejecting H# when true," which directly defines a Type I error. Study Guide references
/topics: hypothesis testing, null hypothesis, Type I error, significance level.
NEW QUESTION # 111
The average commute time for workers in a city in 2021 was 35 minutes, with a standard deviation of 5 minutes.
Assuming a normal distribution, which two values encompass 95% of the data?
Answer: C
Explanation:
For a normally distributed variable, the empirical rule states that approximately 95% of observations fall within two standard deviations of the mean. The mean commute time is 35 minutes, and the standard deviation is 5 minutes. Two standard deviations equal 2 × 5 = 10 minutes. Therefore, the interval covering approximately 95% of the data is 35 # 10 to 35 + 10, which gives 25 minutes to 45 minutes. Option B, 30 to
40 minutes, represents only one standard deviation from the mean and would cover approximately 68% of the data, not 95%. Option A extends three standard deviations from the mean and would correspond to roughly
99.7% under the empirical rule. Option D is not centered properly around the mean and does not represent a standard normal interval. The correct interval is symmetric about the mean and uses the standard deviation as the spread measure. References/topics from the Study Guide: normal distribution, empirical rule, mean, standard deviation.
NEW QUESTION # 112
Review the following inequality:
y < x # 1/2
Which shaded portion in the graphs corresponds to this inequality?
Answer: A
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 # 113
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