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| Section | Weight | Objectives |
|---|---|---|
| Topic 1: Descriptive Statistics | 25% | - Measures of spread: range, IQR, variance, standard deviation - Graphical displays: histograms, boxplots, scatterplots - Measures of center: mean, median, mode - Types of data: categorical, discrete, continuous |
| Topic 2: Correlation & Regression | 20% | - Predictions and limitations of regression - Correlation coefficient and interpretation - Interpreting slope, intercept, and R-squared - Simple linear regression models |
| Topic 3: Inferential Statistics & Study Design | 20% | - Observational studies vs experiments - Hypothesis testing framework and interpretation - Confidence intervals for means/proportions - Sampling methods and bias |
| Topic 4: Basic Numeracy & Algebra | 15% | - Arithmetic operations, fractions, decimals, percentages - Exponents, roots, and basic formulas - Linear equations, inequalities, graphing functions |
| Topic 5: Probability Concepts | 20% | - Conditional probability and Venn diagrams - Discrete and continuous probability distributions - Probability rules, independent and dependent events - Normal distribution and empirical rule |
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NEW QUESTION # 141
Two independent events: P(A) = 0.3, P(B) = 0.2. P(A or B) = ?
Answer: D
Explanation:
For two events, the general addition rule is P(A or B) = P(A) + P(B) # P(A and B). Because A and B are independent, their joint probability is P(A and B) = P(A)P(B). Here, P(A) = 0.3 and P(B) = 0.2, so P(A and B)
= 0.3 × 0.2 = 0.06. Then P(A or B) = 0.3 + 0.2 # 0.06 = 0.44. The subtraction is necessary because the overlap, where both A and B occur, is counted twice when adding P(A) and P(B). Option A, 0.5, incorrectly adds the two probabilities without correcting for overlap. Option B gives the probability of both events, not either event. Option D is unrelated to the addition rule. Study Guide references/topics: independent events, addition rule, multiplication rule, union of events.
NEW QUESTION # 142
Sample correlation r = 0.6. R² = ?
Answer: B
Explanation:
The coefficient of determination, R², is obtained by squaring the correlation coefficient r in simple linear regression. Here, r = 0.6, so R² = (0.6)² = 0.36. This means that 36% of the variability in the response variable is explained by the linear relationship with the explanatory variable. The remaining 64% of variability is not explained by that linear model and may be due to other variables, random variation, measurement error, or nonlinear structure. Option B gives the correlation itself, not its square. Option C would come from squaring
0.4, not 0.6. Option D would imply a perfect explanatory relationship, which would require |r| = 1. The value of R² is always between 0 and 1 and is commonly interpreted as a proportion of explained variation. Study Guide references/topics: correlation, coefficient of determination, regression, explained variation.
NEW QUESTION # 143
Which measure of central tendency is least affected by outliers?
Answer: D
Explanation:
The median is the measure of central tendency least affected by outliers because it depends only on the ordered position of values, not on the numerical magnitude of extreme observations. To find the median, the data are arranged from least to greatest and the middle value is identified, or the average of the two middle values is taken when the sample size is even. If an extremely large or extremely small value is added to a data set, the mean can shift substantially because every value contributes to the arithmetic average. The median, however, usually remains stable unless the extreme value changes the middle position. The mode is also not directly affected by magnitude, but it may be absent or non-unique and is often less informative for numerical data. Range is not a measure of central tendency and is highly sensitive to outliers because it uses the minimum and maximum. Study Guide references/topics: descriptive statistics, measures of center, median, resistance to outliers.
NEW QUESTION # 144
Mean of Poisson # = 5 = ?
Answer: C
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 # 145
In a standard normal distribution, z-score for the mean = ?
Answer: A
Explanation:
A z-score measures how many standard deviations a value is above or below the mean. The formula is z = (x
# #) / #, where x is the observed value, # is the mean, and # is the standard deviation. If the observed value equals the mean, then x = #. Substituting into the formula gives z = (# # #) / # = 0 / # = 0. Therefore, the z- score corresponding to the mean is always 0 in any normal distribution, including the standard normal distribution. In the standard normal distribution specifically, the mean is 0 and the standard deviation is 1, so the mean lies exactly at z = 0. A z-score of 1 would indicate one standard deviation above the mean, and #1 would indicate one standard deviation below the mean. Study Guide references/topics: standard normal distribution, z-scores, mean, standard deviation.
NEW QUESTION # 146
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