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| Section | Weight | Objectives |
|---|---|---|
| Topic 1: Correlation & Regression | 20% | - Simple linear regression models - Predictions and limitations of regression - Interpreting slope, intercept, and R-squared - Correlation coefficient and interpretation |
| Topic 2: Probability Concepts | 20% | - Conditional probability and Venn diagrams - Probability rules, independent and dependent events - Normal distribution and empirical rule - Discrete and continuous probability distributions |
| Topic 3: Inferential Statistics & Study Design | 20% | - Hypothesis testing framework and interpretation - Observational studies vs experiments - Sampling methods and bias - Confidence intervals for means/proportions |
| Topic 4: Basic Numeracy & Algebra | 15% | - Linear equations, inequalities, graphing functions - Exponents, roots, and basic formulas - Arithmetic operations, fractions, decimals, percentages |
| Topic 5: Descriptive Statistics | 25% | - Types of data: categorical, discrete, continuous - Graphical displays: histograms, boxplots, scatterplots - Measures of center: mean, median, mode - Measures of spread: range, IQR, variance, standard deviation |
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NEW QUESTION # 96
The dot plot illustrates the frequency of outdoor games played by students per week.
Which statement is true?
Answer: D
Explanation:
The dot plot shows a distribution centered near 3 days, with substantial frequencies at 2, 3, and 4 days and smaller frequencies at the extremes of 1 and 5 days. This shape is reasonably balanced around the center.
When a distribution is approximately symmetric, the mean and median tend to be close because the lower and higher values balance each other. The median identifies the middle observation after the data are ordered, and the mean represents the balance point of the distribution. Since the tallest stack is near 3 days and the surrounding stacks on 2 and 4 days are comparable, the center of the data is approximately 3 days by both measures. There is no strong skew to pull the mean far above or below the median. Therefore, the best statement is that the mean is almost the same as the median. Options B and C would require clear skew or extreme imbalance, which the dot plot does not show. References/topics from the Study Guide: dot plots, mean, median, distribution shape, symmetry.
NEW QUESTION # 97
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: B
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 # 98
A standard deck of 52 playing cards, 13 with hearts, 13 with diamonds, 13 with clovers, and 13 with spades, is shuffled, and one card is drawn at random.
What is the probability of drawing a heart?
Answer: C
Explanation:
The probability of a simple event is calculated by dividing the number of favorable outcomes by the total number of equally likely outcomes. A standard deck contains 52 cards. The favorable outcomes are the hearts, and the question states that there are 13 hearts in the deck. Therefore, the probability of drawing a heart is 13
/52. This fraction simplifies by dividing both numerator and denominator by 13, giving 1/4. Option A, 1/13, would incorrectly treat one card as favorable out of 13 rather than 13 favorable hearts out of 52 total cards.
Option B, 1/2, would imply that half the deck consists of hearts, which is false. Option D, 1/3, does not correspond to the four equally sized suits in a standard deck. Since the four suits are equally represented, each suit has probability one out of four. References/topics from the Study Guide: theoretical probability, equally likely outcomes, fractions, sample spaces.
NEW QUESTION # 99
A teacher plots the test scores of a class using the box plot.
What is true about the test scores?
Answer: A
Explanation:
A box plot displays the five-number summary of a quantitative data set: minimum, first quartile, median, third quartile, and maximum. The median is represented by the vertical line inside the box. In the given box plot, that internal vertical line is positioned at 80 on the score axis. Therefore, the median test score for Class A is
80 points. The value 70 corresponds to the left edge of the box, which represents the first quartile, not the median. The value near 88 represents the right edge of the box, which is the third quartile. The whiskers extend to the approximate minimum and maximum scores, but those values do not determine the median. The median divides the ordered data into two equal halves, meaning about 50% of the students scored at or below
80 and about 50% scored at or above 80. References/topics from the Study Guide: box plots, five-number summary, median, quartiles.
NEW QUESTION # 100
Regression slope indicates:
Answer: D
Explanation:
In a linear regression equation, the slope represents the predicted change in the response variable Y for each one-unit increase in the explanatory variable X. In slope-intercept form, # = b# + b#x, the slope is b#. For example, if a regression equation predicts cost as # = 25 + 4x, the slope 4 means the predicted cost increases by 4 units for each additional unit of x. The intercept, b#, is the predicted value of Y when X = 0, so option B describes a different component. R² measures the proportion of variation in Y explained by the regression model, not the rate of change. Correlation measures strength and direction of linear association, but it is not the same as the slope because it is unitless and standardized. The slope is the operational rate of change in the model. Study Guide references/topics: linear regression, slope interpretation, response variable, explanatory variable.
NEW QUESTION # 101
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