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| Section | Weight | Objectives |
|---|---|---|
| Topic 1: Descriptive Statistics | 25% | - Measures of spread: range, IQR, variance, standard deviation - Measures of center: mean, median, mode - Graphical displays: histograms, boxplots, scatterplots - Types of data: categorical, discrete, continuous |
| Topic 2: Inferential Statistics & Study Design | 20% | - Hypothesis testing framework and interpretation - Observational studies vs experiments - Confidence intervals for means/proportions - Sampling methods and bias |
| Topic 3: Correlation & Regression | 20% | - Predictions and limitations of regression - Interpreting slope, intercept, and R-squared - Correlation coefficient and interpretation - Simple linear regression models |
| Topic 4: Probability Concepts | 20% | - Conditional probability and Venn diagrams - Discrete and continuous probability distributions - Normal distribution and empirical rule - Probability rules, independent and dependent events |
| 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 # 17
Probability of drawing red card from deck = ?
Answer: D
Explanation:
A standard deck has 52 cards divided into four suits: hearts, diamonds, clubs, and spades. Hearts and diamonds are red, while clubs and spades are black. Each suit has 13 cards, so the number of red cards is 13 +
13 = 26. The probability of drawing a red card is therefore the number of favorable outcomes divided by the total number of outcomes: 26/52. This simplifies to 1/2. Option B, 1/4, would describe the probability of drawing one specific suit, such as hearts only. Option C, 1/13, would describe one specific rank in the deck, such as a particular value across suits. Option D does not correspond to the card structure of a standard deck.
Since exactly half the deck is red, the correct probability is 26/52 = 1/2. Study Guide references/topics: card probability, favorable outcomes, sample space, theoretical probability.
NEW QUESTION # 18
Probability it does NOT rain = 1 # 0.25 = ?
Answer: C
NEW QUESTION # 19
A golf course is attempting to correlate golfing handicap with math SAT scores among local high school golfers. Ignoring potential confounding variables such as socioeconomic status, the golf course creates the following scatterplot.
What is the estimated value of r, the correlation coefficient, between these variables?
Answer: A
Explanation:
The correlation coefficient r measures the direction and strength of a linear relationship between two quantitative variables. In the scatterplot, the points are widely dispersed, so the relationship is weak rather than strong. The fitted trend line slopes slightly downward, indicating a negative association: as golf handicap increases, math SAT score tends to decrease slightly. Because the pattern is weak and negative, r should be close to 0 but less than 0. The best match is #0.10. Option A, #0.63, would represent a moderately strong negative linear relationship, which would require the points to cluster more tightly around a downward- sloping line. Option C, 0.10, has the right weak magnitude but the wrong direction because it is positive.
Option D, 0.63, is both too strong and positive. The visual evidence supports only a very slight negative linear association. References/topics from the Study Guide: scatterplots, correlation coefficient, positive and negative association, strength of linear relationship.
NEW QUESTION # 20
Z-score = ?
Answer: A
Explanation:
A z-score standardizes a raw value by expressing its distance from the mean in standard deviation units. The formula is z = (x # #)/#, where x is the observed value, # is the mean, and # is the standard deviation. The numerator x # # measures how far the value is from the mean. Dividing by # converts that distance into standard deviation units. A positive z-score means the value is above the mean, a negative z-score means the value is below the mean, and z = 0 means the value equals the mean. Option B divides the raw value by the mean and does not measure standardized distance. Option C reverses the ratio incorrectly. Option D gives only the raw deviation and fails to standardize by the standard deviation. Z-scores are central in normal distribution calculations and comparisons across different scales. Study Guide references/topics: z-score, standardization, mean, standard deviation.
NEW QUESTION # 21
A home inspector finds 3% of the homes in a community infected with termites.
How should the home inspector's findings be interpreted?
Answer: B
Explanation:
A probability or percentage describes how often an event is expected to occur in the long run. Here, 3% of homes are infected with termites. As a probability, this is 0.03, meaning about 3 out of every 100 homes would be expected to have termites. This is a small probability, so the event should be interpreted as unlikely.
It is not impossible, because impossible would require a probability of 0%. It is also not likely, because likely events generally have probabilities substantially greater than 50%. Finally, it is not "as likely as unlikely," because that language corresponds to a probability near 50%, where occurrence and nonoccurrence are approximately balanced. Since 3% is close to zero but not equal to zero, the technically correct interpretation is that termite infection is unlikely for a randomly selected home in the community. References/topics from the Study Guide: probability interpretation, percentages, unlikely events, complementary probability.
NEW QUESTION # 22
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