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| Section | Weight | Objectives |
|---|---|---|
| Correlation & Regression | 20% | - Simple linear regression models - Interpreting slope, intercept, and R-squared - Predictions and limitations of regression - Correlation coefficient and interpretation |
| Basic Numeracy & Algebra | 15% | - Linear equations, inequalities, graphing functions - Exponents, roots, and basic formulas - Arithmetic operations, fractions, decimals, percentages |
| Probability Concepts | 20% | - Discrete and continuous probability distributions - Probability rules, independent and dependent events - Conditional probability and Venn diagrams - Normal distribution and empirical rule |
| Descriptive Statistics | 25% | - Measures of spread: range, IQR, variance, standard deviation - Types of data: categorical, discrete, continuous - Graphical displays: histograms, boxplots, scatterplots - Measures of center: mean, median, mode |
| Inferential Statistics & Study Design | 20% | - Hypothesis testing framework and interpretation - Observational studies vs experiments - Sampling methods and bias - Confidence intervals for means/proportions |
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86. Frage
A researcher has collected information on students from a school. The researcher wants to display the ethnic groups represented in the school.
Which pair of graphs both display data in this manner?
Antwort: C
Begründung:
Ethnic group is a categorical variable because it classifies students into named groups rather than measuring a numerical quantity. Categorical data are commonly displayed with bar graphs or pie charts. A bar graph shows the frequency or relative frequency of each category using separate bars, making it easy to compare group sizes. A pie chart shows how the whole student population is divided among categories, making it useful for displaying proportions or percentages. Therefore, the correct pair is bar graph and pie chart. A box plot is used for quantitative data and summarizes values using quartiles and a median, so it is not appropriate for ethnic categories. A line graph is typically used to show change over time or ordered numerical trends. A histogram is used for distributions of quantitative data grouped into intervals, not named categories. Since the goal is to display category membership, both selected graphs must support categorical frequency or percentage displays. References/topics from the Study Guide: categorical data displays, bar graphs, pie charts, relative frequency.
87. Frage
Regression R² = 0.64. Interpretation?
Antwort: D
Begründung:
The coefficient of determination, R², measures the proportion of variability in the response variable Y that is explained by the regression model using explanatory variable X. If R² = 0.64, then 64% of the variation in Y is explained by its linear relationship with X. The remaining 36% is unexplained by the model and may reflect other variables, random variation, measurement error, or nonlinear patterns. Option B is incorrect because R² is not the same as correlation. In simple linear regression, correlation r would be either +0.8 or #0.8, depending on the slope direction, because r² = 0.64. Option C is incorrect because the slope measures change in Y per one-unit change in X, not explained variation. Option D is incorrect because R² is not a probability of making a correct prediction. It is a proportion of variation accounted for by the model. Study Guide references
/topics: regression, coefficient of determination, explained variation, linear modeling.
88. Frage
A university surveys faculty and students to determine support for a new campus recycling initiative.
The results of the survey are shown in the following 2 × 2 contingency table:
Which statement is true?
Antwort: A
Begründung:
This problem compares conditional percentages across two groups. For faculty members, 40 out of 50 support the recycling initiative, so the faculty support rate is 40/50 = 0.80, or 80%. For students, 200 out of 500 support the initiative, so the student support rate is 200/500 = 0.40, or 40%. Comparing 80% and 40% shows that faculty members are twice as likely as students to support the initiative. This is not a slight difference; it is a large difference of 40 percentage points. Therefore, the correct statement is that faculty members are much more likely than students to support the recycling initiative. The table contains two categorical variables: group type and recycling opinion. Conditional percentages are the appropriate numerical tool because the goal is to compare support within each group. References/topics from the Study Guide:
contingency tables, two-way categorical data, conditional percentages, comparative proportions.
89. Frage
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?
Antwort: C
Begründung:
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.
90. Frage
There are 10 green, 20 yellow, and 15 purple marbles in a jar.
What is the probability of selecting 2 green marbles in a row and then 1 yellow marble, replacing the marble each time?
Antwort: C
Begründung:
There are 10 green, 20 yellow, and 15 purple marbles, so the total number of marbles is 10 + 20 + 15 = 45.
Because each marble is replaced after selection, the probabilities remain the same on every draw, making the events independent. The probability of selecting a green marble on one draw is 10/45 = 2/9. Selecting two green marbles in a row gives (2/9)(2/9). The probability of then selecting a yellow marble is 20/45 = 4/9.
Multiply the probabilities because the question asks for green and green and yellow in that exact sequence: (2
/9)(2/9)(4/9) = 16/729. Replacement is essential; without replacement, the denominators and numerators would change after each draw. Since replacement keeps the sample space constant at 45 marbles each time, the independent multiplication rule applies directly. References/topics from the Study Guide: independent events, replacement, multiplication rule, compound probability.
91. Frage
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