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| Section | Weight | Objectives |
|---|---|---|
| Inferential Statistics & Study Design | 20% | - Confidence intervals for means/proportions - Hypothesis testing framework and interpretation - Observational studies vs experiments - Sampling methods and bias |
| Basic Numeracy & Algebra | 15% | - Exponents, roots, and basic formulas - Linear equations, inequalities, graphing functions - Arithmetic operations, fractions, decimals, percentages |
| Correlation & Regression | 20% | - Correlation coefficient and interpretation - Interpreting slope, intercept, and R-squared - Simple linear regression models - Predictions and limitations of regression |
| Descriptive Statistics | 25% | - Measures of center: mean, median, mode - Measures of spread: range, IQR, variance, standard deviation - Types of data: categorical, discrete, continuous - Graphical displays: histograms, boxplots, scatterplots |
| Probability Concepts | 20% | - Probability rules, independent and dependent events - Conditional probability and Venn diagrams - Discrete and continuous probability distributions - Normal distribution and empirical rule |
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NEW QUESTION # 13
Z-score negative #
Answer: B
Explanation:
A z-score measures how many standard deviations a data value is from the mean. The formula is z = (x # #)/#, where x is the observed value, # is the mean, and # is the standard deviation. Since standard deviation is positive, the sign of the z-score depends on the numerator, x # #. If x is less than the mean, then x # # is negative, producing a negative z-score. Therefore, a negative z-score indicates that the observed value is below the mean. A positive z-score indicates a value above the mean, while a z-score of 0 indicates a value exactly equal to the mean. Option D is incorrect because the sign of the z-score gives direct positional information relative to the mean. Study Guide references/topics: z-scores, standard normal distribution, mean, standard deviation.
NEW QUESTION # 14
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 # 15
There are 14 black, 16 white, and 10 red balls in a box.
What is the probability of selecting 1 black ball, then 1 red ball, and then 1 white ball, replacing the ball each time?
Answer: D
Explanation:
The box contains 14 black, 16 white, and 10 red balls, for a total of 40 balls. Because the ball is replaced after each selection, the probability of each color remains constant on every draw. This makes the three draws independent. The probability of selecting a black ball first is 14/40, which simplifies to 7/20. The probability of selecting a red ball second is 10/40, or 1/4. The probability of selecting a white ball third is 16/40, or 2/5.
Since the question asks for all three events in the stated order, multiply the probabilities: (7/20)(1/4)(2/5) = 14
/400 = 7/200. Replacement is the controlling condition; without replacement, the denominators would decrease after each draw. Here, the sample space remains 40 each time. References/topics from the Study Guide: probability, independent events, replacement, multiplication rule.
NEW QUESTION # 16
Which graph displays data in a manner that is accurate?
Answer: A
Explanation:
The accurate display is the bar graph labeled "Number of Feet Traveled" with the vertical axis showing the number of feet and the horizontal axis identifying the student travelers. For discrete observations associated with individual students, a bar graph is appropriate because each bar represents a separate category or individual and its height represents the measured value. Option A is inaccurate because its title states
"Number of Miles Traveled," while the vertical axis is labeled in feet; this creates a unit mismatch. Option C uses a pie chart, which is designed to show parts of a whole, not individual measured distances unless the goal is proportional composition. Option D uses a line graph, which is typically reserved for ordered change, especially over time; connecting student traveler values implies continuity or trend that is not justified. The correct graph must use consistent units, clear labels, and an appropriate display type. References/topics from the Study Guide: data displays, bar graphs, categorical identifiers, quantitative measurements, graph accuracy.
NEW QUESTION # 17
t-test used when:
Answer: C
Explanation:
A t-test is used when making inferences about a population mean and the population standard deviation, #, is unknown. In practical settings, # is rarely available, so the sample standard deviation, s, is used as an estimate.
That substitution introduces additional uncertainty, which is why the t-distribution is used instead of the standard normal distribution. The t-distribution has heavier tails, especially for small samples, reflecting the extra variability caused by estimating # from the sample. Option B describes a z-test setting, where the population standard deviation is known. Option C is incorrect because categorical population data are usually analyzed with proportions, chi-square tests, or related categorical procedures, not mean-based t-tests. Option D is invalid because t-tests have a clear inferential role. The controlling condition is unknown #, with inference focused on means. Study Guide references/topics: t-tests, unknown population standard deviation, sample standard deviation, inferential statistics.
NEW QUESTION # 18
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