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| Section | Objectives |
|---|---|
| Statistical Inference | - Hypothesis testing
|
| Probability | - Probability rules
|
| Descriptive Statistics | - Data summarization
|
| Regression and Correlation | - Relationship analysis
|
| Probability Distributions | - Discrete distributions
|
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NEW QUESTION # 151
Conditional probability formula:
Answer: C
Explanation:
Conditional probability measures the probability that event A occurs given that event B has already occurred.
The formula is P(A|B) = P(A and B)/P(B), assuming P(B) is greater than zero. The denominator P(B) restricts the sample space to cases where B occurs, and the numerator P(A and B) counts cases where both A and B occur within that restricted space. Option B is incorrect because it divides P(A) by P(B) without requiring overlap between A and B. Option C reverses the conditioning and would relate to P(B|A) only if the numerator were P(A and B). Option D applies to independent events when finding P(A and B), not to conditional probability in general. The vertical bar in P(A|B) is read as "given," and it signals that the denominator should be the probability of the given event. Study Guide references/topics: conditional probability, joint probability, event intersection, probability rules.
NEW QUESTION # 152
A class of 25 students includes 10 who play soccer, 8 who play basketball, and 7 who play neither sport.
What is the probability of randomly selecting a student who does not play soccer?
Answer: A
Explanation:
The probability of selecting a student who does not play soccer is found by identifying the complement of the soccer group. There are 25 students in the class, and 10 students play soccer. Therefore, the number of students who do not play soccer is 25 # 10 = 15. The probability is then the number of favorable outcomes divided by the total number of possible outcomes: 15/25 = 0.60. The information about basketball and neither sport provides context, but the direct complement method is sufficient because the question asks only who does not play soccer. Option B, .40, represents the probability of selecting a student who does play soccer, since 10/25 = .40. Option A, .30, is associated with neither sport if interpreted approximately from 7/25, but it is not the requested event. Option C, .50, does not match the count structure. References/topics from the Study Guide: probability, complements, favorable outcomes, relative frequency.
NEW QUESTION # 153
Regression R² = 0.64. Interpretation?
Answer: D
Explanation:
The coefficient of determination, R², measures the proportion of variability in the response variable Y that is explained by the regression model using explanatory variable X. If R² = 0.64, then 64% of the variation in Y is explained by its linear relationship with X. The remaining 36% is unexplained by the model and may reflect other variables, random variation, measurement error, or nonlinear patterns. Option B is incorrect because R² is not the same as correlation. In simple linear regression, correlation r would be either +0.8 or #0.8, depending on the slope direction, because r² = 0.64. Option C is incorrect because the slope measures change in Y per one-unit change in X, not explained variation. Option D is incorrect because R² is not a probability of making a correct prediction. It is a proportion of variation accounted for by the model. Study Guide references
/topics: regression, coefficient of determination, explained variation, linear modeling.
NEW QUESTION # 154
What percent of data lies within 2 standard deviations of the mean in a normal distribution?
Answer: D
Explanation:
For a normal distribution, the empirical rule, also called the 68-95-99.7 rule, describes how data are distributed around the mean. Approximately 68% of observations fall within 1 standard deviation of the mean, approximately 95% fall within 2 standard deviations, and approximately 99.7% fall within 3 standard deviations. The question asks specifically for the percentage within 2 standard deviations, so the correct value is 95%. This interval is written as # # 2# to # + 2#, where # is the mean and # is the standard deviation.
Option B corresponds to one standard deviation, not two. Option C is an imprecise version of the three- standard-deviation rule, and option D has no standard empirical-rule interpretation in this context. This rule is frequently used to estimate ranges in bell-shaped distributions. Study Guide references/topics: normal distribution, empirical rule, standard deviation, distribution spread.
NEW QUESTION # 155
In a normal distribution, 95% of data lies within:
Answer: D
Explanation:
For a normal distribution, the empirical rule states that approximately 68% of data fall within one standard deviation of the mean, approximately 95% fall within two standard deviations, and approximately 99.7% fall within three standard deviations. The notation ±2 SD means two standard deviations below the mean to two standard deviations above the mean, or # # 2# to # + 2#. Therefore, the interval containing about 95% of normally distributed observations is ±2 standard deviations. Option B corresponds to approximately 68%, not
95%. Option C corresponds to approximately 99.7%, and option D extends beyond the standard empirical- rule benchmarks. This concept is central when estimating the typical spread of bell-shaped data, such as test scores, biological measurements, or repeated measurement errors. The correct answer is ±2 SD because it matches the 95% portion of the 68-95-99.7 rule. Study Guide references/topics: normal distribution, empirical rule, standard deviation, distribution spread.
NEW QUESTION # 156
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