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| Section | Weight | Objectives |
|---|---|---|
| Probability Concepts | 20% | - Normal distribution and empirical rule - Conditional probability and Venn diagrams - Probability rules, independent and dependent events - Discrete and continuous probability distributions |
| Descriptive Statistics | 25% | - Measures of center: mean, median, mode - Measures of spread: range, IQR, variance, standard deviation - Graphical displays: histograms, boxplots, scatterplots - Types of data: categorical, discrete, continuous |
| Inferential Statistics & Study Design | 20% | - Hypothesis testing framework and interpretation - Confidence intervals for means/proportions - Sampling methods and bias - Observational studies vs experiments |
| Basic Numeracy & Algebra | 15% | - Arithmetic operations, fractions, decimals, percentages - Linear equations, inequalities, graphing functions - Exponents, roots, and basic formulas |
| Correlation & Regression | 20% | - Interpreting slope, intercept, and R-squared - Simple linear regression models - Predictions and limitations of regression - Correlation coefficient and interpretation |
>> Real Applied-Probability-and-Statistics Questions <<
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NEW QUESTION # 22
The dot plot illustrates the frequency of outdoor games played by students per week.
Which statement is true?
Answer: D
Explanation:
The dot plot shows a distribution centered near 3 days, with substantial frequencies at 2, 3, and 4 days and smaller frequencies at the extremes of 1 and 5 days. This shape is reasonably balanced around the center.
When a distribution is approximately symmetric, the mean and median tend to be close because the lower and higher values balance each other. The median identifies the middle observation after the data are ordered, and the mean represents the balance point of the distribution. Since the tallest stack is near 3 days and the surrounding stacks on 2 and 4 days are comparable, the center of the data is approximately 3 days by both measures. There is no strong skew to pull the mean far above or below the median. Therefore, the best statement is that the mean is almost the same as the median. Options B and C would require clear skew or extreme imbalance, which the dot plot does not show. References/topics from the Study Guide: dot plots, mean, median, distribution shape, symmetry.
NEW QUESTION # 23
What is the result of 2/5 + 1/3 # 1/4?
Answer: D
Explanation:
To add and subtract fractions, first rewrite all fractions using a common denominator. The denominators are
5, 3, and 4. Their least common denominator is 60. Convert each fraction: 2/5 = 24/60, 1/3 = 20/60, and 1/4 =
15/60. Now combine the numerators while keeping the common denominator: 24/60 + 20/60 # 15/60 = (24 +
20 # 15)/60 = 29/60. The fraction 29/60 is already in simplest form because 29 is prime and does not divide
60. Option A, 13/60, and option B, 11/60, result from incorrect numerator operations. Option D, 19/60, also fails to preserve the correct addition before subtraction. The essential technical step is establishing a common denominator before performing arithmetic operations. References/topics from the Study Guide: fractions, least common denominator, fraction addition, fraction subtraction.
NEW QUESTION # 24
Standard error decreases when:
Answer: A
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 # 25
Empirical probability is based on:
Answer: B
Explanation:
Empirical probability is based on observed data collected from experiments, surveys, simulations, or repeated trials. It is calculated as the relative frequency of an event: number of times the event occurs divided by the total number of trials or observations. For example, if a machine produces 12 defective items in a sample of
300, the empirical probability of a defect is 12/300 = 0.04. This differs from classical or theoretical probability, which is based on equally likely outcomes and mathematical structure, such as a fair die having probability 1/6 for each face. It also differs from subjective probability, which is based on personal judgment or expert belief rather than observed frequency. The word "empirical" signals evidence obtained through observation, so observed frequency is the correct basis. Study Guide references/topics: empirical probability, relative frequency, observed data, probability interpretation.
NEW QUESTION # 26
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?
Answer: D
Explanation:
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.
NEW QUESTION # 27
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