Math Problem Statement
Fill in the blank. Events that are _______ cannot occur at the same time. Question content area bottom Part 1 Events that are ▼ unusual double-counted independent disjoint cannot occur at the same time. Which of the following corresponds to the case when every sample of size n has the same chance of being chosen? Question content area bottom Part 1 Choose the correct answer below. Which measure of variation is most sensitive to extreme values? Question content area bottom Part 1 Choose the correct answer below.
Histogram
Range
Median
Mean Random sample
Simple random sample
Experiment Which of the following is NOT a voluntary response sample? Question content area bottom Part 1 Choose the correct answer below. A. A survey is taken at a mall by asking passersby if they will fill out the survey. In what sense are the mean, median, mode, and midrange measures of "center"? Question content area bottom Part 1 Choose the correct answer below. A. They use different approaches for providing a value (or values) of the center or middle of the sorted list of data. B. Question content area top Part 1 Fill in the blank. The square of the standard deviation is called the _______. Question content area bottom Part 1 The square of the standard deviation is called the ▼ dispersion. variance. mean. spread. They are all the four values in the center of a sorted list of data. C. They are the most common values in the data set. D. They use different approaches for providing the same value (or values) of the center or middle of the sorted list of data. B. A radio station asks for call-in responses to a question concerning city recycling. C. A local dentist asks her patients to fill out a questionnaire and mail it back to determine the quality of the care received during an office visit. D. Quiz scores from a college level statistics course are analyzed to determine student progress.
Probability sample Let event Aequals=subject is telling the truth and event Bequals=polygraph test indicates that the subject is lying. Use your own words to translate the notation Upper P left parenthesis B|A right parenthesisP(B|A) into a verbal statement. Question content area bottom Part 1 Choose the correct option below. A. The probability that the polygraph indicates lying given that the subject is actually lying. B. The probability that the polygraph indicates truthfulness given that the subject is actually lying. C. The probability that the polygraph indicates lying given that the subject is actually telling the truth. D. The probability that the polygraph indicates truthfulness given that the subject is actually telling the truth.
Solution
Here's a breakdown of each question with the correct answers:
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Events that are _______ cannot occur at the same time.
- Answer: Disjoint
- Explanation: Disjoint (or mutually exclusive) events cannot occur at the same time because they have no outcomes in common.
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Which of the following corresponds to the case when every sample of size has the same chance of being chosen?
- Answer: Simple random sample
- Explanation: A simple random sample ensures that every possible sample of the specified size has an equal chance of being selected.
-
Which measure of variation is most sensitive to extreme values?
- Answer: Range
- Explanation: The range, which is the difference between the maximum and minimum values, is sensitive to extreme values as it directly depends on these values.
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Which of the following is NOT a voluntary response sample?
- Answer: D. Quiz scores from a college-level statistics course are analyzed to determine student progress.
- Explanation: A voluntary response sample relies on individuals volunteering to participate, but analyzing pre-existing quiz scores does not require voluntary participation from students.
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In what sense are the mean, median, mode, and midrange measures of "center"?
- Answer: A. They use different approaches for providing a value (or values) of the center or middle of the sorted list of data.
- Explanation: These measures each represent a central point of a data set but use different approaches, like averaging or identifying the middlemost value.
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The square of the standard deviation is called the _______.
- Answer: Variance
- Explanation: Variance is the square of the standard deviation and measures the spread of a data set.
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Translate in a verbal statement given : subject is telling the truth and : polygraph test indicates that the subject is lying.
- Answer: C. The probability that the polygraph indicates lying given that the subject is actually telling the truth.
- Explanation: represents the probability of event occurring given that has occurred.
Would you like further details on any answer, or have any additional questions?
Here are five related questions to expand on these concepts:
- What distinguishes disjoint events from independent events in probability?
- How does a simple random sample differ from a stratified random sample?
- Why is variance used in statistics, and how does it relate to standard deviation?
- How might outliers affect measures of central tendency like the mean versus the median?
- What are the implications of using a voluntary response sample in a survey?
Tip: In probability and statistics, always distinguish between different sampling methods to understand how each affects data quality and reliability.
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Math Problem Analysis
Mathematical Concepts
Probability
Statistics
Sampling Methods
Measures of Central Tendency
Measures of Variation
Formulas
Variance = (Standard Deviation)^2
P(B|A) - Conditional Probability Formula
Theorems
Basic Probability Theorems
Concepts of Disjoint Events
Conditional Probability Theory
Suitable Grade Level
Grades 10-12
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