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| Section | Weight | Objectives |
|---|---|---|
| Topic 1: Descriptive Statistics | 25% | - Measures of center: mean, median, mode - Types of data: categorical, discrete, continuous - Measures of spread: range, IQR, variance, standard deviation - Graphical displays: histograms, boxplots, scatterplots |
| Topic 2: Inferential Statistics & Study Design | 20% | - Sampling methods and bias - Confidence intervals for means/proportions - Hypothesis testing framework and interpretation - Observational studies vs experiments |
| Topic 3: Probability Concepts | 20% | - Discrete and continuous probability distributions - Probability rules, independent and dependent events - Conditional probability and Venn diagrams - Normal distribution and empirical rule |
| Topic 4: Correlation & Regression | 20% | - Interpreting slope, intercept, and R-squared - Correlation coefficient and interpretation - Simple linear regression models - Predictions and limitations of regression |
| Topic 5: Basic Numeracy & Algebra | 15% | - Arithmetic operations, fractions, decimals, percentages - Linear equations, inequalities, graphing functions - Exponents, roots, and basic formulas |
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107. Frage
Confidence interval = sample mean ± ?
Antwort: B
Begründung:
A confidence interval for a population mean is generally constructed as sample mean ± margin of error. The margin of error equals a critical value multiplied by the standard error. Therefore, the structure is sample mean ± critical value × SE. The critical value depends on the confidence level and distribution used, such as a z critical value when the population standard deviation is known or a t critical value when it is unknown. The standard error measures the sampling variability of the sample mean, often computed as s/#n when using sample standard deviation. Option B is incorrect because variance times sample size is not a margin of error.
Option C is incomplete because standard deviation alone measures spread among data values, not uncertainty of the sample mean. Option D is incorrect because the median is a measure of center and is not the typical component of a mean-based confidence interval. Study Guide references/topics: confidence intervals, standard error, critical value, margin of error.
108. Frage
A t-distribution is used when:
Antwort: D
Begründung:
A t-distribution is used for inference about a population mean when the population standard deviation # is unknown, especially with a small sample. In that situation, the sample standard deviation s must estimate #, creating extra uncertainty. The t-distribution accounts for this added uncertainty with heavier tails than the standard normal distribution. As sample size increases, the t-distribution becomes closer to the normal distribution. Option B describes a z-procedure setting, where # is known and the normal distribution may be used. Option C is incorrect because categorical data are usually analyzed with proportions or chi-square procedures, not t-distributions for means. Option D is incomplete: t-procedures typically require quantitative continuous or approximately continuous data, but the decisive condition in the answer set is unknown # with a small sample. Study Guide references/topics: t-distribution, unknown standard deviation, small samples, inference for means.
109. Frage
Dataset: 3, 5, 7, 9, 11. Median = ?
Antwort: D
Begründung:
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.
110. Frage
Type II error # is:
Antwort: C
Begründung:
A Type II error occurs when the null hypothesis is false but the test fails to reject it. Many introductory answer choices phrase this as "accept H# when false," though the more technically careful wording is "fail to reject H# when false." This is a false negative: the real effect or difference exists, but the test does not detect sufficient evidence. The probability of a Type II error is denoted #. Option B describes a Type I error, which is rejecting a true null hypothesis. Option C is incorrect because 1 # # is not #; # is the Type I error probability, while 1 # # is statistical power. Option D is too vague and does not identify a formal hypothesis- testing error. The defining condition for Type II error is missing a real effect by failing to reject a false null hypothesis. Study Guide references/topics: Type II error, beta, hypothesis testing, statistical power.
111. Frage
Given a normal distribution with a mean of 40 and a standard deviation of 6, what is the range that contains approximately 95% of the data?
Antwort: D
Begründung:
For a normal distribution, the empirical rule states that approximately 95% of the data fall within two standard deviations of the mean. The mean is 40, and the standard deviation is 6. Two standard deviations equal 2 × 6
= 12. To construct the 95% interval, subtract and add 12 from the mean: 40 # 12 = 28 and 40 + 12 = 52.
Therefore, the range containing approximately 95% of the data is 28 to 52. Option D, 34 to 46, represents one standard deviation from the mean and corresponds to about 68% of the data. Option B, 22 to 58, represents three standard deviations from the mean and corresponds to approximately 99.7% of the data. Option C is not based on the stated standard deviation. The correct interval must be symmetric around the mean and extend exactly two standard deviations in each direction. References/topics from the Study Guide: normal distribution, empirical rule, mean, standard deviation.
112. Frage
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