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| Section | Weight | Objectives |
|---|---|---|
| Topic 1: Descriptive Statistics | 25% | - Graphical displays: histograms, boxplots, scatterplots - Measures of spread: range, IQR, variance, standard deviation - Types of data: categorical, discrete, continuous - Measures of center: mean, median, mode |
| Topic 2: Probability Concepts | 20% | - Discrete and continuous probability distributions - Conditional probability and Venn diagrams - Normal distribution and empirical rule - Probability rules, independent and dependent events |
| Topic 3: Inferential Statistics & Study Design | 20% | - Confidence intervals for means/proportions - Hypothesis testing framework and interpretation - Observational studies vs experiments - Sampling methods and bias |
| Topic 4: Correlation & Regression | 20% | - Correlation coefficient and interpretation - Predictions and limitations of regression - Interpreting slope, intercept, and R-squared - Simple linear regression models |
| Topic 5: Basic Numeracy & Algebra | 15% | - Exponents, roots, and basic formulas - Arithmetic operations, fractions, decimals, percentages - Linear equations, inequalities, graphing functions |
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NEW QUESTION # 12
In a class of 30 students, 18 are enrolled in a math course, and 12 are enrolled in a science course. Among the students enrolled in the science course, 8 are also enrolled in the math course.
What is the probability that a student is enrolled in the math course given that they are enrolled in the science course?
Answer: C
Explanation:
The phrase "given that they are enrolled in the science course" indicates conditional probability. The reference group is not all 30 students; it is only the 12 students enrolled in science. Among those 12 science students, 8 are also enrolled in math. Therefore, the conditional probability is P(math | science) = P(math and science) ÷ P(science), or more directly, 8 ÷ 12. This simplifies to 2/3, which is approximately 0.6667, rounded to .67. Option A, .27, would come from comparing the 8 students to the entire class of 30, but that ignores the given condition. Option B, .40, corresponds to 12/30, the proportion enrolled in science. Option C, .44, is approximately 8/18, which reverses the condition and would represent the probability of science given math.
The correct answer uses the science group as the denominator. References/topics from the Study Guide:
conditional probability, two-way events, joint enrollment, probability ratios.
NEW QUESTION # 13
Z-test used when:
Answer: C
Explanation:
A z-test for a population mean is used when the population standard deviation # is known and the sampling distribution of the test statistic can be treated as normal. The test statistic has the form z = (sample statistic # hypothesized parameter) divided by the standard error. Knowing # allows the standard error to be computed using #/#n rather than estimating it with the sample standard deviation. Option B describes the common setting for a t-test, not a z-test. Option C is not sufficient by itself; small samples generally require stronger normality assumptions and often favor t-procedures when # is unknown. Option D is unrelated to the classic z- test for a mean, though z-tests can also be used for proportions under appropriate large-sample conditions. In the provided answer set, the defining condition is that the population standard deviation is known. Study Guide references/topics: z-test, population standard deviation, standard error, hypothesis testing.
NEW QUESTION # 14
Dataset: 3, 5, 7, 9, 11. Median = ?
Answer: D
Explanation:
The median is the center value of an ordered dataset. The values 3, 5, 7, 9, and 11 are already arranged from least to greatest. Because there are five observations, the median is the third value, with two observations below it and two observations above it. The third value is 7, so the median is 7. The median is a measure of central tendency that describes the middle position of the data rather than the arithmetic average. In this dataset, the mean is also 7 because the values are evenly spaced around 7, but the median is determined by position, not by summing and dividing. Option B is the second value, option C is the fourth value, and option D is not a data value. The correct answer is the value that splits the ordered list into two equal halves. Study Guide references/topics: median, ordered data, measures of center, descriptive statistics.
NEW QUESTION # 15
Standard error decreases when:
Answer: C
Explanation:
The standard error of the sample mean is calculated as SE = s/#n, where s is the sample standard deviation and n is the sample size. Since n appears in the denominator, increasing the sample size reduces the standard error, assuming the standard deviation stays constant. This reflects the fact that larger samples produce more stable estimates of the population mean. Option B is incorrect because decreasing sample size increases standard error. Option C is incorrect because a larger standard deviation increases standard error by increasing the numerator. Option D is incorrect because the mean affects the center of the distribution but does not directly determine the standard error. Standard error is about precision: smaller standard error means less sampling variability and a more precise estimate. That is why larger samples are preferred in inference. Study Guide references/topics: standard error, sample size, standard deviation, sampling variability.
NEW QUESTION # 16
Conditional probability P(A|B) = P(A and B)/P(B) #
Answer: B
Explanation:
The formula for conditional probability is P(A|B) = P(A and B)/P(B), provided P(B) > 0. The notation P(A|B) is read as "the probability of A given B." The denominator P(B) restricts the sample space to cases in which B occurs, and the numerator P(A and B) counts the portion of that restricted group in which A also occurs.
Therefore, the statement is true. Option B is incorrect because the formula is the standard definition of conditional probability. Option C is incorrect because if A and B are mutually exclusive, then P(A and B) = 0, which creates a special case rather than the general definition. Option D is invalid because conditional probability is undefined when P(B) = 0. The condition must have positive probability. Study Guide references
/topics: conditional probability, joint probability, event intersection, probability rules.
NEW QUESTION # 17
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