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| Section | Weight | Objectives |
|---|---|---|
| Basic Numeracy & Algebra | 15% | - Linear equations, inequalities, graphing functions - Exponents, roots, and basic formulas - Arithmetic operations, fractions, decimals, percentages |
| Probability Concepts | 20% | - Normal distribution and empirical rule - Probability rules, independent and dependent events - Conditional probability and Venn diagrams - Discrete and continuous probability distributions |
| Descriptive Statistics | 25% | - Graphical displays: histograms, boxplots, scatterplots - Types of data: categorical, discrete, continuous - Measures of center: mean, median, mode - Measures of spread: range, IQR, variance, standard deviation |
| Correlation & Regression | 20% | - Interpreting slope, intercept, and R-squared - Simple linear regression models - Predictions and limitations of regression - Correlation coefficient and interpretation |
| Inferential Statistics & Study Design | 20% | - Hypothesis testing framework and interpretation - Sampling methods and bias - Confidence intervals for means/proportions - Observational studies vs experiments |
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NEW QUESTION # 119
Standard deviation increases #
Answer: A
Explanation:
Standard deviation measures how far data values typically fall from the mean. When standard deviation increases, the data are more spread out. This means individual observations tend to be farther from the mean, producing greater variability. A smaller standard deviation means the data values are more tightly clustered around the mean. Option B states the opposite of the correct interpretation. Option C is incorrect because an increase in standard deviation does not necessarily mean the mean increases; center and spread are separate features of a distribution. Option D is also incorrect because variance is the square of standard deviation, so if standard deviation increases, variance increases as well, not decreases. Standard deviation is useful because it is expressed in the same units as the original data, making spread easier to interpret. Study Guide references
/topics: standard deviation, variance, spread, measures of variability.
NEW QUESTION # 120
Correlation coefficient r = #0.9 indicates:
Answer: C
Explanation:
The correlation coefficient r measures the direction and strength of a linear relationship between two quantitative variables. It ranges from #1 to 1. A value close to #1 indicates a strong negative linear relationship, meaning that as one variable increases, the other tends to decrease in a highly consistent linear pattern. Since r = #0.9 is very close to #1, the relationship is strong and negative. Option B is incorrect because the sign is negative, not positive. Option C identifies the direction correctly but understates the strength; #0.9 is not weak. Option D would correspond to r near 0, where there is little or no linear association. A scatterplot associated with r = #0.9 would show points clustered closely around a downward- sloping line. This does not prove causation; it describes linear association only. Study Guide references
/topics: correlation coefficient, negative association, strength of relationship, scatterplots.
NEW QUESTION # 121
A dataset: 2, 4, 6, 8, 10. Variance = ?
Answer: C
Explanation:
Variance measures the average squared distance of data values from the mean. For the dataset 2, 4, 6, 8, 10, the mean is (2 + 4 + 6 + 8 + 10) ÷ 5 = 30 ÷ 5 = 6. The deviations from the mean are #4, #2, 0, 2, and 4.
Squaring these deviations gives 16, 4, 0, 4, and 16. The sum of squared deviations is 40. Using the sample variance formula, divide by n # 1, where n = 5. Thus, sample variance = 40 ÷ 4 = 10. Option A is correct.
Option C, 6.25, does not result from the standard sample variance computation for these values. The important distinction is whether a problem is using sample variance or population variance; the provided answer set and calculation use the sample variance formula. Study Guide references/topics: variance, mean, squared deviations, sample variance.
NEW QUESTION # 122
Chi-square test used for:
Answer: A
Explanation:
A chi-square test is commonly used to analyze categorical data, especially to determine whether two categorical variables are associated. In a chi-square test of independence, data are arranged in a contingency table, and observed cell counts are compared with expected cell counts under the assumption that the variables are independent. If the observed counts differ substantially from the expected counts, there is evidence of association between the categorical variables. For example, a chi-square test could examine whether voting preference is associated with age group or whether product preference differs by region.
Option B describes comparing means, which is typically handled by a t-test or related procedure. Option C refers to regression, which models relationships between variables, often involving quantitative outcomes.
Option D refers to variance, which is tested using different procedures depending on context. The key phrase is "categorical variables": chi-square methods work with counts in categories. Study Guide references/topics:
categorical data, contingency tables, chi-square test, association.
NEW QUESTION # 123
Mean of Poisson # = 5 = ?
Answer: D
Explanation:
For a Poisson distribution, the parameter # represents the mean number of events occurring in a fixed interval.
Therefore, if # = 5, the mean is 5. This means that over many repeated intervals of the same size, the long-run average number of events per interval would be 5. The Poisson distribution is used for count data, such as calls per hour, accidents per week, or defects per batch, when events occur independently and at a constant average rate. A special property of the Poisson distribution is that its variance also equals #, so in this case the variance would also be 5. However, the question asks for the mean, so the direct answer is 5. Options B, C, and D are not supported by the stated parameter. Study Guide references/topics: Poisson distribution, # parameter, expected value, count data.
NEW QUESTION # 124
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