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| Section | Weight | Objectives |
|---|---|---|
| Topic 1: 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 2: Inferential Statistics & Study Design | 20% | - Sampling methods and bias - Confidence intervals for means/proportions - Hypothesis testing framework and interpretation - Observational studies vs experiments |
| Topic 3: Descriptive Statistics | 25% | - Measures of center: mean, median, mode - Types of data: categorical, discrete, continuous - Measures of spread: range, IQR, variance, standard deviation - Graphical displays: histograms, boxplots, scatterplots |
| Topic 4: Correlation & Regression | 20% | - Predictions and limitations of regression - Interpreting slope, intercept, and R-squared - Simple linear regression models - Correlation coefficient and interpretation |
| Topic 5: Basic Numeracy & Algebra | 15% | - Arithmetic operations, fractions, decimals, percentages - Exponents, roots, and basic formulas - Linear equations, inequalities, graphing functions |
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NEW QUESTION # 136
A cafe recorded the total ice cream sales and the average maximum temperature of the day. The scatterplot shows the recorded data. The regression equation y = 13x # 598 estimates the total ice cream sales, y, of a day and the average maximum temperature, x, on that day.
What does the slope represent in this context?
Answer: B
Explanation:
In a linear regression equation of the form y = mx + b, the slope m gives the predicted change in the response variable y for a one-unit increase in the explanatory variable x. Here, y represents total ice cream sales and x represents average maximum temperature. The equation y = 13x # 598 has slope 13, so the model predicts that ice cream sales increase by about $13 for every 1°F increase in temperature. This is not the sales value at
0°F; that would be the intercept, #598, which is generally not meaningful in this practical context. It is also not the predicted sales at 100°F, because that would require substituting x = 100 into the regression equation.
The positive slope matches the upward trend in the scatterplot: higher temperatures are associated with higher ice cream sales. References/topics from the Study Guide: correlation and regression, slope interpretation, explanatory and response variables.
NEW QUESTION # 137
Two dice rolled. Probability sum = 7?
Answer: D
Explanation:
When two standard six-sided dice are rolled, there are 6 × 6 = 36 equally likely ordered outcomes. To find the probability that the sum is 7, count all ordered pairs that produce 7. These are (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1). There are 6 favorable outcomes. Therefore, the probability is 6/36, which simplifies to 1/6. Since the answer choices include both 6/36 and 1/6, the listed answer from the PDF uses the unsimplified equivalent form, 6/36. Option C, 5/36, omits one valid ordered pair. Option D, 1/12, is too small because it would represent only 3 favorable outcomes out of 36. This problem reinforces that dice outcomes are ordered when two dice are rolled, so (1,6) and (6,1) are counted separately. Study Guide references/topics: sample spaces, dice probability, favorable outcomes, theoretical probability.
NEW QUESTION # 138
Two independent events: P(A) = 0.3, P(B) = 0.2. P(A or B) = ?
Answer: D
Explanation:
For two events, the general addition rule is P(A or B) = P(A) + P(B) # P(A and B). Because A and B are independent, their joint probability is P(A and B) = P(A)P(B). Here, P(A) = 0.3 and P(B) = 0.2, so P(A and B)
= 0.3 × 0.2 = 0.06. Then P(A or B) = 0.3 + 0.2 # 0.06 = 0.44. The subtraction is necessary because the overlap, where both A and B occur, is counted twice when adding P(A) and P(B). Option A, 0.5, incorrectly adds the two probabilities without correcting for overlap. Option B gives the probability of both events, not either event. Option D is unrelated to the addition rule. Study Guide references/topics: independent events, addition rule, multiplication rule, union of events.
NEW QUESTION # 139
Boxplot shows:
Answer: C
Explanation:
A boxplot summarizes the distribution of a quantitative variable using key positional statistics. It displays the median, first quartile, third quartile, and typically the minimum and maximum non-outlier values. It may also mark outliers separately. The box itself spans from Q1 to Q3, representing the interquartile range, or middle
50% of the data. The line inside the box marks the median. Whiskers extend to values within the non-outlier range, depending on the graphing convention. A boxplot does not primarily show frequency counts; histograms, dot plots, and bar charts are better for frequencies. A scatterplot displays the relationship between two quantitative variables. Probability is not directly displayed by a standard boxplot, although distributional interpretation can be supported by it. The correct answer is therefore median, quartiles, and outliers. Study Guide references/topics: boxplots, five-number summary, quartiles, outliers.
NEW QUESTION # 140
95% CI = 50 ± 2. SE = ?
Answer: D
Explanation:
A confidence interval has the structure estimate ± margin of error. The margin of error is calculated as critical value × standard error. For a 95% confidence interval using the normal approximation, the critical value is approximately 1.96, often rounded to 2 in introductory settings. The interval is given as 50 ± 2, so the margin of error is 2. Using the approximate 95% critical value of 2, we solve 2 = 2 × SE, giving SE = 1. More exactly, using 1.96 gives SE = 2/1.96 # 1.02, which rounds to 1. Option B confuses the margin of error with the standard error. Option C is too large, and option D would produce a margin of error near 1 under a 95% critical value. The correct standard error is approximately 1. Study Guide references/topics: confidence intervals, standard error, critical value, margin of error.
NEW QUESTION # 141
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