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| Section | Weight | Objectives |
|---|---|---|
| Correlation & Regression | 20% | - Interpreting slope, intercept, and R-squared - Simple linear regression models - Predictions and limitations of regression - Correlation coefficient and interpretation |
| Inferential Statistics & Study Design | 20% | - Hypothesis testing framework and interpretation - Confidence intervals for means/proportions - Observational studies vs experiments - Sampling methods and bias |
| Basic Numeracy & Algebra | 15% | - Exponents, roots, and basic formulas - Linear equations, inequalities, graphing functions - Arithmetic operations, fractions, decimals, percentages |
| Descriptive Statistics | 25% | - Measures of center: mean, median, mode - Graphical displays: histograms, boxplots, scatterplots - Measures of spread: range, IQR, variance, standard deviation - Types of data: categorical, discrete, continuous |
| Probability Concepts | 20% | - Normal distribution and empirical rule - Discrete and continuous probability distributions - Conditional probability and Venn diagrams - Probability rules, independent and dependent events |
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NEW QUESTION # 115
Type II error occurs when:
Answer: C
Explanation:
A Type II error occurs when the null hypothesis is false but the statistical test fails to reject it. In many answer choices, this is expressed as "accepting the null when false," though the more precise language is "failing to reject the null." This error is a false negative: the test misses a real effect, difference, or relationship. For example, if a medication truly improves recovery but a study fails to detect sufficient evidence of improvement, that is a Type II error. Option B describes a Type I error, which occurs when a true null hypothesis is rejected. Option C is not an error. Option D is too vague; statistical decision errors refer specifically to incorrect conclusions about hypotheses, not ordinary data-entry mistakes. The probability of a Type II error is denoted #, and statistical power is 1 # #. Study Guide references/topics: hypothesis testing, Type II error, null hypothesis, statistical power.
NEW QUESTION # 116
Standard deviation increases #
Answer: B
Explanation:
Standard deviation measures how far data values typically fall from the mean. When standard deviation increases, the data are more spread out. This means individual observations tend to be farther from the mean, producing greater variability. A smaller standard deviation means the data values are more tightly clustered around the mean. Option B states the opposite of the correct interpretation. Option C is incorrect because an increase in standard deviation does not necessarily mean the mean increases; center and spread are separate features of a distribution. Option D is also incorrect because variance is the square of standard deviation, so if standard deviation increases, variance increases as well, not decreases. Standard deviation is useful because it is expressed in the same units as the original data, making spread easier to interpret. Study Guide references
/topics: standard deviation, variance, spread, measures of variability.
NEW QUESTION # 117
In a city's public transportation system, the distribution of commuters by mode of transport is as follows: 40% use buses, 25% use trains, 20% use bicycles, 10% walk, and 5% use other means of transportation.
What is the probability that a randomly selected commuter uses either a bus or a train?
Answer: B
Explanation:
The event is that a randomly selected commuter uses either a bus or a train. These categories are mutually exclusive because one commuter is classified under one primary transportation mode in the given distribution.
For mutually exclusive events, the probability of "A or B" is found by adding the individual probabilities. The probability of using a bus is 40%, and the probability of using a train is 25%. Therefore, P(bus or train) = 40%
+ 25% = 65%. The bicycle, walking, and other transportation categories are not included because the question restricts the event to bus or train only. Option B, 45%, would incorrectly combine bus with the 5% "other" category or otherwise omit part of the train group. Option C is too low, and option A is unrelated to the stated categories. References/topics from the Study Guide: probability, mutually exclusive events, addition rule, percentage distributions.
NEW QUESTION # 118
Sample mean = 60; point estimate of population mean = ?
Answer: A
Explanation:
A point estimate is a single sample statistic used to estimate an unknown population parameter. When estimating a population mean, the standard point estimate is the sample mean. In this question, the sample mean is given as 60. Therefore, the point estimate of the population mean is also 60. This does not mean the true population mean is guaranteed to equal 60; rather, 60 is the best single numerical estimate based on the available sample. Confidence intervals build on this point estimate by adding and subtracting a margin of error to reflect sampling uncertainty. Option B is incorrect because although the true population mean is unknown, the point estimate is known. Option C and option D do not correspond to the sample statistic provided. The logic is central to inferential statistics: use sample evidence to estimate population characteristics. Study Guide references/topics: sample mean, population mean, point estimation, inferential statistics.
NEW QUESTION # 119
Probability of rolling sum = 2 on 2 dice = ?
Answer: D
Explanation:
When two standard six-sided dice are rolled, there are 6 × 6 = 36 equally likely ordered outcomes. To get a sum of 2, the only possible ordered pair is (1, 1). No other pair of die faces can produce a total of 2 because 1 is the smallest value on each die. Therefore, there is 1 favorable outcome out of 36 total outcomes, giving a probability of 1/36. Option B, 1/6, is the probability of one specific result on a single die, not a two-dice sum.
Option C, 2/36, would require two favorable ordered pairs, but only one exists. Option D, 1/12, is also too large because it corresponds to 3 outcomes out of 36. The key is to count ordered outcomes in the full two- dice sample space. Study Guide references/topics: dice probability, sample space, favorable outcomes, theoretical probability.
NEW QUESTION # 120
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