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| Section | Objectives |
|---|---|
| Topic 1: Statistical Inference | - Estimation
|
| Topic 2: Regression and Correlation | - Relationship analysis
|
| Topic 3: Descriptive Statistics | - Data summarization
|
| Topic 4: Probability | - Probability rules
|
| Topic 5: Probability Distributions | - Continuous distributions
|
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NEW QUESTION # 112
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 # 113
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 # 114
Correlation coefficient r = #0.9 indicates:
Answer: A
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 # 115
Correlation r = 0.8 # strong positive relationship #
Answer: C
Explanation:
A correlation coefficient of r = 0.8 indicates a strong positive linear relationship between two quantitative variables. The positive sign means that as one variable increases, the other tends to increase. The magnitude,
0.8, is close to 1, which indicates a strong linear pattern. It is not perfect, because perfect positive correlation would be r = 1, but it is clearly stronger than a weak or moderate association. Option B is incorrect because the interpretation matches both the sign and magnitude of r. Option C is incorrect because correlation is used for quantitative variables, not categorical variables. Option D is incorrect because a negative r would indicate a negative relationship. Importantly, correlation does not prove causation; it describes the direction and strength of linear association. Study Guide references/topics: correlation coefficient, positive association, linear relationship, scatterplot interpretation.
NEW QUESTION # 116
The pie chart shows the contribution of different renewable energy sources to the total energy production.
What is true about the given data?
Answer: D
Explanation:
A pie chart displays how a whole is divided into categorical parts, usually as percentages totaling 100%. The chart shows solar at 35%, hydropower at 30%, wind at 20%, geothermal at 10%, and biomass at 5%. The largest percentage is solar, so solar power contributes the most to total energy production. Option A is false because hydropower plus biomass equals 30% + 5% = 35%, which is equal to solar, not more than solar.
Option B is false because geothermal is 10%, while biomass is only 5%; therefore, biomass contributes the least. Option C is false because biomass plus geothermal equals 5% + 10% = 15%, which is less than wind at
20%. The correct interpretation requires comparing category percentages accurately rather than relying on visual size alone. References/topics from the Study Guide: pie charts, categorical data, percentages, interpreting graphical displays.
NEW QUESTION # 117
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