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| Section | Weight | Objectives |
|---|---|---|
| Topic 1: Correlation & Regression | 20% | - Predictions and limitations of regression - Simple linear regression models - Correlation coefficient and interpretation - Interpreting slope, intercept, and R-squared |
| Topic 2: Probability Concepts | 20% | - Discrete and continuous probability distributions - Normal distribution and empirical rule - Conditional probability and Venn diagrams - Probability rules, independent and dependent events |
| Topic 3: Inferential Statistics & Study Design | 20% | - Hypothesis testing framework and interpretation - Observational studies vs experiments - Confidence intervals for means/proportions - Sampling methods and bias |
| Topic 4: Descriptive Statistics | 25% | - Measures of spread: range, IQR, variance, standard deviation - Types of data: categorical, discrete, continuous - Measures of center: mean, median, mode - Graphical displays: histograms, boxplots, scatterplots |
| Topic 5: Basic Numeracy & Algebra | 15% | - Linear equations, inequalities, graphing functions - Exponents, roots, and basic formulas - Arithmetic operations, fractions, decimals, percentages |
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NEW QUESTION # 112
The table shows the results of a survey of favorite movie genres.
What is the probability of selecting an action and then a comedy respondent if the selection is replaced?
Answer: B
Explanation:
Because the first selection is replaced, the two selections are independent. Replacement means the probability structure returns to its original state after the first respondent is selected. The probability of selecting an action respondent is 30%, or 0.30. The probability of selecting a comedy respondent is 35%, or 0.35. For independent sequential events, multiply the probabilities: 0.30 × 0.35 = 0.105. Converting 0.105 to a percentage gives 10.5%. Therefore, the probability of first selecting an action respondent and then selecting a comedy respondent is 10.5%. Option B does not result from multiplying the two relevant genre percentages.
Options C and D are far too large because they resemble combined or unrelated percentages rather than the probability of a two-step ordered selection. The word "and" signals multiplication, while "replacement" confirms independence between draws. References/topics from the Study Guide: independent events, replacement, multiplication rule, probability with percentages.
NEW QUESTION # 113
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: D
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 # 114
A recording studio raises its use fee to $75 and charges $40 per hour for studio time. The equation of the total cost of a recording session as a function of studio time is y = 40x + 75.
Which graph represents this equation?
Answer: A
Explanation:
The equation y = 40x + 75 is written in slope-intercept form, y = mx + b. In this form, m represents the rate of change and b represents the initial value. The constant term 75 means the graph must cross the y-axis at 75, because the studio charges $75 before any hourly time is added. The coefficient 40 means that for every additional hour of studio time, the total cost increases by $40. Therefore, the correct graph must begin at y =
75 when x = 0 and rise at a steady linear rate of 40 dollars per hour. For example, at x = 6 hours, the model gives y = 40(6) + 75 = 315, so the line should pass near the point (6, 315). Among the displayed graphs, Graph 4 matches both the y-intercept and the slope. References/topics from the Study Guide: basic algebra, linear equations, slope-intercept form, interpreting rate of change.
NEW QUESTION # 115
Mean = 100, SD = 15, z = 2. Value = ?
Answer: A
Explanation:
A z-score expresses how many standard deviations a value lies above or below the mean. The formula is z = (x # #)/#. To solve for the raw value x, rearrange the formula: x = # + z#. Here, the mean # is 100, the standard deviation # is 15, and z = 2. Substitute these values: x = 100 + 2(15) = 100 + 30 = 130. Therefore, the raw value is 130. This means the value is two standard deviations above the mean. Option B, 115, would correspond to z = 1. Option C, 125, is not exactly two standard deviations above 100 when # = 15. Option D,
110, is less than one standard deviation above the mean. The correct value must add two full standard deviations to the mean. Study Guide references/topics: z-scores, standardization, normal distribution, raw score conversion.
NEW QUESTION # 116
A city council surveys residents and business owners about a proposed new public transportation system. The results of the survey are shown in the following 2 × 2 contingency table.
Which statement is true?
Answer: D
Explanation:
This question requires comparing conditional percentages from a two-way table. For residents, 150 out of 200 are in favor of the proposed transportation system. The resident support rate is therefore 150/200 = 0.75, or
75%. For business owners, 30 out of 100 are in favor. The business owner support rate is 30/100 = 0.30, or
30%. The difference is 75% # 30% = 45 percentage points, which is a large gap. Therefore, a resident is much more likely than a business owner to favor the new transportation system. Option A understates the magnitude of the difference by calling it slight. Options B and C reverse the direction of the comparison because residents have the higher support rate, not the lower one. The appropriate statistical tool here is conditional percentage because support is being compared within each respondent group. References/topics from the Study Guide: contingency tables, conditional percentages, two-variable categorical data, comparative proportions.
NEW QUESTION # 117
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