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| Section | Weight | Objectives |
|---|---|---|
| Topic 1: Basic Numeracy & Algebra | 15% | - Arithmetic operations, fractions, decimals, percentages - Linear equations, inequalities, graphing functions - Exponents, roots, and basic formulas |
| Topic 2: Probability Concepts | 20% | - Discrete and continuous probability distributions - Normal distribution and empirical rule - Probability rules, independent and dependent events - Conditional probability and Venn diagrams |
| Topic 3: Inferential Statistics & Study Design | 20% | - Observational studies vs experiments - Sampling methods and bias - Confidence intervals for means/proportions - Hypothesis testing framework and interpretation |
| Topic 4: Correlation & Regression | 20% | - Correlation coefficient and interpretation - Simple linear regression models - Predictions and limitations of regression - Interpreting slope, intercept, and R-squared |
| 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 # 60
Standard error decreases when:
Answer: B
Explanation:
The standard error of the mean is calculated as SE = s/#n, where s is the sample standard deviation and n is the sample size. Because n appears in the denominator under a square root, increasing the sample size decreases the standard error when the standard deviation is held constant. This reflects a central idea in sampling: larger samples tend to produce more stable and precise estimates of the population mean. Option C is incorrect because increasing the standard deviation increases the standard error, not decreases it. Option B is incomplete and does not identify what is decreasing. Option D is not the direct driver of standard error; confidence level affects the critical value and margin of error, but the standard error itself is determined by variability and sample size. The correct relationship is inverse: as sample size increases, standard error decreases. Study Guide references/topics: standard error, sample size, sampling variability, precision of estimates.
NEW QUESTION # 61
Sample mean = 40, SD = 8, n = 16. Standard error = ?
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. Here, the standard deviation is 8 and the sample size is 16. The square root of 16 is 4, so SE = 8/4 = 2. The sample mean of 40 is not used directly in the standard error formula; it identifies the center of the sample, not the variability of the sample mean across repeated samples. Option B, 8, is the standard deviation, not the standard error. Option D, 4, is the square root of the sample size. Option C, 0.5, would result from an incorrect calculation. Standard error decreases as sample size increases because larger samples provide more precise estimates. Study Guide references/topics: standard error, standard deviation, sample size, sampling distribution.
NEW QUESTION # 62
Type I error # = 0.05 means:
Answer: C
Explanation:
The symbol # represents the significance level of a hypothesis test and is the probability of making a Type I error. A Type I error occurs when the null hypothesis is true but the test rejects it. Therefore, # = 0.05 means there is a 5% risk of rejecting a true null hypothesis under the testing procedure. This is often described as the false positive rate. Option B describes a Type II error, which involves failing to reject a false null hypothesis.
Option C is incorrect because a 5% significance level corresponds to a 95% confidence level in related confidence-interval contexts, not 5% confidence. Option D is unrelated; # is not a sample-size percentage.
The interpretation must connect # directly to the probability of incorrectly rejecting H# when H# is actually true. Study Guide references/topics: hypothesis testing, significance level, Type I error, null hypothesis.
NEW QUESTION # 63
Standard deviation squared = ?
Answer: D
Explanation:
Variance and standard deviation are directly connected measures of spread. Variance is calculated by averaging squared deviations from the mean, while standard deviation is the square root of variance.
Therefore, reversing that relationship, standard deviation squared equals variance. Symbolically, if the standard deviation is s, then the sample variance is s². This relationship matters because variance is expressed in squared units, while standard deviation is expressed in the original units of measurement. For example, if test-score standard deviation is 4 points, the variance is 4² = 16 square points. The mean and median are measures of center, not squared spread. The standard error measures the variability of a sample statistic, usually the sample mean, across repeated samples. The correct answer is variance because it is the squared form of standard deviation. Study Guide references/topics: standard deviation, variance, measures of spread, descriptive statistics.
NEW QUESTION # 64
A teacher compares the test scores of two classes using a box plot.
What is true about the median test scores?
Answer: A
Explanation:
A box plot displays the five-number summary, including the median, which is shown by the vertical line inside each box. In the exhibit, the median for Class A is positioned at approximately 65, while the median for Class B is positioned at approximately 80. The difference is therefore 80 # 65 = 15 points. Since Class A's median is lower, the correct interpretation is that the median test score of Class A is 15 points less than that of Class B. This comparison uses a categorical grouping variable, class, and a quantitative response variable, test score. The box plot is appropriate because it allows the distributions of two groups to be compared visually using medians, quartiles, ranges, and potential spread. Options A, B, and D do not match the median locations shown by the center lines in the boxes. References/topics from the Study Guide: box plots, median, five- number summary, comparing distributions.
NEW QUESTION # 65
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