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| Section | Weight | Objectives |
|---|---|---|
| Topic 1: Correlation & Regression | 20% | - Predictions and limitations of regression - Correlation coefficient and interpretation - Simple linear regression models - Interpreting slope, intercept, and R-squared |
| Topic 2: Descriptive Statistics | 25% | - Types of data: categorical, discrete, continuous - Graphical displays: histograms, boxplots, scatterplots - Measures of spread: range, IQR, variance, standard deviation - Measures of center: mean, median, mode |
| Topic 3: Basic Numeracy & Algebra | 15% | - Exponents, roots, and basic formulas - Linear equations, inequalities, graphing functions - Arithmetic operations, fractions, decimals, percentages |
| Topic 4: Probability Concepts | 20% | - Probability rules, independent and dependent events - Discrete and continuous probability distributions - Normal distribution and empirical rule - Conditional probability and Venn diagrams |
| Topic 5: Inferential Statistics & Study Design | 20% | - Sampling methods and bias - Hypothesis testing framework and interpretation - Confidence intervals for means/proportions - Observational studies vs experiments |
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NEW QUESTION # 26
Variance of Poisson # = 5 = ?
Answer: A
Explanation:
A defining property of the Poisson distribution is that its variance equals its mean, and both are equal to #.
Since the question states # = 5, the variance is also 5. This property distinguishes the Poisson distribution from many other probability distributions. The mean represents the expected number of events per interval, while the variance describes the spread of the event count around that mean. In a Poisson model with # = 5, event counts tend to vary around 5, and the numerical variance is 5. Option B, 4, option C, 0, and option D, 1, do not follow from the Poisson variance rule. The result is not obtained by squaring # or taking its square root; it is simply equal to #. Study Guide references/topics: Poisson distribution, variance, mean, # parameter.
NEW QUESTION # 27
What is the result of 2/5 + 1/3 # 1/4?
Answer: C
Explanation:
To add and subtract fractions, first rewrite all fractions using a common denominator. The denominators are
5, 3, and 4. Their least common denominator is 60. Convert each fraction: 2/5 = 24/60, 1/3 = 20/60, and 1/4 =
15/60. Now combine the numerators while keeping the common denominator: 24/60 + 20/60 # 15/60 = (24 +
20 # 15)/60 = 29/60. The fraction 29/60 is already in simplest form because 29 is prime and does not divide
60. Option A, 13/60, and option B, 11/60, result from incorrect numerator operations. Option D, 19/60, also fails to preserve the correct addition before subtraction. The essential technical step is establishing a common denominator before performing arithmetic operations. References/topics from the Study Guide: fractions, least common denominator, fraction addition, fraction subtraction.
NEW QUESTION # 28
A team of scientists wants to understand the relationship between smoking and lung cancer. They collect data from 1,000 individuals, recording their smoking habits and whether they have been diagnosed with lung cancer. The scientists then analyze the data to find any correlations.
Is this study observational or experimental?
Answer: C
Explanation:
This is an observational study because the scientists collect existing information about individuals' smoking habits and lung cancer diagnoses without assigning treatments or controlling exposure. In an experimental study, researchers impose a condition, treatment, or intervention and then measure the resulting effect. Here, the researchers are not requiring some individuals to smoke and others not to smoke; they are simply recording naturally occurring characteristics and outcomes. The purpose is to examine association, or correlation, between two variables: smoking status and lung cancer diagnosis. Both variables are categorical, so the analysis would likely involve proportions, conditional percentages, or contingency tables. Option A is incorrect because analyzing correlations does not make a study experimental. Option B is incorrect because
"testing effects" would require manipulation or assignment. Option C identifies a true feature, a large sample size, but sample size does not determine study type. References/topics from the Study Guide: observational studies, experimental studies, association, categorical variables.
NEW QUESTION # 29
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 # 30
Sample correlation r = 0.6. R² = ?
Answer: B
Explanation:
The coefficient of determination, R², is obtained by squaring the correlation coefficient r in simple linear regression. Here, r = 0.6, so R² = (0.6)² = 0.36. This means that 36% of the variability in the response variable is explained by the linear relationship with the explanatory variable. The remaining 64% of variability is not explained by that linear model and may be due to other variables, random variation, measurement error, or nonlinear structure. Option B gives the correlation itself, not its square. Option C would come from squaring
0.4, not 0.6. Option D would imply a perfect explanatory relationship, which would require |r| = 1. The value of R² is always between 0 and 1 and is commonly interpreted as a proportion of explained variation. Study Guide references/topics: correlation, coefficient of determination, regression, explained variation.
NEW QUESTION # 31
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