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| Section | Objectives |
|---|---|
| Statistical Inference | - Hypothesis Testing (Introductory Level)
|
| Descriptive Statistics | - Two Variable Data Analysis
|
| Probability Theory | - Probability Distributions
|
| Regression and Modeling | - Linear Relationships
|
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NEW QUESTION # 107
Uniform distribution 0-5: P(X < 3) = ?
Answer: B
Explanation:
For a continuous uniform distribution on the interval from 0 to 5, probability is proportional to interval length.
The total interval length is 5 # 0 = 5. The event X < 3 corresponds to the interval from 0 to 3, which has length 3. Therefore, P(X < 3) = 3/5 = 0.6. This works because the uniform distribution assigns constant density across the entire interval, so any subinterval's probability equals its length divided by the total length.
Option B would correspond to half the interval, such as X < 2.5. Option C would correspond to length 2 out of
5. Option D incorrectly treats the cutoff value 3 as if it were a percentage rather than an interval boundary.
The correct answer is 0.6, meaning 60% of the uniform distribution lies below 3. Study Guide references
/topics: uniform distribution, continuous probability, interval length, probability density.
NEW QUESTION # 108
A researcher has collected information on students from a school. The researcher wants to display the ethnic groups represented in the school.
Which pair of graphs both display data in this manner?
Answer: B
Explanation:
Ethnic group is a categorical variable because it classifies students into named groups rather than measuring a numerical quantity. Categorical data are commonly displayed with bar graphs or pie charts. A bar graph shows the frequency or relative frequency of each category using separate bars, making it easy to compare group sizes. A pie chart shows how the whole student population is divided among categories, making it useful for displaying proportions or percentages. Therefore, the correct pair is bar graph and pie chart. A box plot is used for quantitative data and summarizes values using quartiles and a median, so it is not appropriate for ethnic categories. A line graph is typically used to show change over time or ordered numerical trends. A histogram is used for distributions of quantitative data grouped into intervals, not named categories. Since the goal is to display category membership, both selected graphs must support categorical frequency or percentage displays. References/topics from the Study Guide: categorical data displays, bar graphs, pie charts, relative frequency.
NEW QUESTION # 109
Empirical probability = ?
Answer: C
Explanation:
Empirical probability is probability determined from observed data rather than from a purely theoretical model. It is calculated by dividing the number of times an event actually occurs by the total number of trials or observations. For example, if a basketball player makes 72 free throws in 100 attempts, the empirical probability of a made free throw is 72/100 = 0.72. This differs from theoretical probability, which is derived from known equally likely outcomes, such as rolling a 3 on a fair six-sided die. It also differs from a guess or subjective estimate because empirical probability requires actual recorded evidence. The term "uniform" describes a distribution in which outcomes or intervals have equal probability, not the basis for empirical probability. Since the question asks for the definition of empirical probability, the correct selection is observed data. Study Guide references/topics: empirical probability, relative frequency, observed outcomes, probability interpretation.
NEW QUESTION # 110
The table shows the results of a survey of favorite movie genres.
What is the probability of selecting an action and then a comedy respondent if the selection is replaced?
Answer: C
Explanation:
Because the first selection is replaced, the two selections are independent. Replacement means the probability structure returns to its original state after the first respondent is selected. The probability of selecting an action respondent is 30%, or 0.30. The probability of selecting a comedy respondent is 35%, or 0.35. For independent sequential events, multiply the probabilities: 0.30 × 0.35 = 0.105. Converting 0.105 to a percentage gives 10.5%. Therefore, the probability of first selecting an action respondent and then selecting a comedy respondent is 10.5%. Option B does not result from multiplying the two relevant genre percentages.
Options C and D are far too large because they resemble combined or unrelated percentages rather than the probability of a two-step ordered selection. The word "and" signals multiplication, while "replacement" confirms independence between draws. References/topics from the Study Guide: independent events, replacement, multiplication rule, probability with percentages.
NEW QUESTION # 111
Correlation coefficient r = #0.9 indicates:
Answer: D
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 # 112
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