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Questions and Answers
A continuity correction is made to a discrete whole number, such as x, in the binomial distribution. Which of the following intervals would we use to represent x?
A continuity correction is made to a discrete whole number, such as x, in the binomial distribution. Which of the following intervals would we use to represent x?
x - 0.5 to x + 0.5
Which of the following is NOT a conclusion of the Central Limit Theorem?
Which of the following is NOT a conclusion of the Central Limit Theorem?
Which of the following is NOT a property of the sampling distribution of the variance?
Which of the following is NOT a property of the sampling distribution of the variance?
Which statement below indicates the area to the left of 19.5 before a continuity correction is used?
Which statement below indicates the area to the left of 19.5 before a continuity correction is used?
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Why must a continuity correction be used when using the normal approximation for the binomial distribution?
Why must a continuity correction be used when using the normal approximation for the binomial distribution?
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Which of the following is NOT a requirement for using the normal distribution as an approximation to the binomial distribution?
Which of the following is NOT a requirement for using the normal distribution as an approximation to the binomial distribution?
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Which of the following is a biased estimator? That is, which of the following does not target the population parameter?
Which of the following is a biased estimator? That is, which of the following does not target the population parameter?
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The Rare Event Rule for Inferential Statistics states that if, under a given assumption, the probability of a particular observed event is exceptionally small (such as less than 0.05), then we conclude __________.
The Rare Event Rule for Inferential Statistics states that if, under a given assumption, the probability of a particular observed event is exceptionally small (such as less than 0.05), then we conclude __________.
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Which of the following is NOT a property of the sampling distribution of the sample mean?
Which of the following is NOT a property of the sampling distribution of the sample mean?
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Study Notes
Continuity Correction
- A continuity correction adjusts discrete values in the binomial distribution by using intervals of x - 0.5 to x + 0.5 to improve the approximation with normal distribution.
Central Limit Theorem
- The Central Limit Theorem asserts that the distribution of sample means will approach a normal distribution as the sample size increases.
Sampling Distribution of Variance
- The sampling distribution of variance does not follow a normal distribution; it tends to be positively skewed, especially in small samples.
Areas in Continuous Distribution
- To represent the area to the left of 19.5 before applying a continuity correction, one would consider "at most 19," focusing on whole numbers.
Importance of Continuity Correction
- Continuity correction is necessary when using normal approximation for the binomial distribution since binomial data is discrete while normal distribution is continuous.
Normal Approximation Requirements
- A normal distribution can be used to approximate a binomial distribution when the trials are independent and not dependent on each other (not the result of dependent trials).
Biased Estimators
- The median is considered a biased estimator because it does not target the population parameter accurately compared to other estimators like the mean.
Rare Event Rule
- According to the Rare Event Rule for Inferential Statistics, if an observed event's probability is extremely low (less than 0.05), it suggests that the initial assumption is likely incorrect.
Properties of Sample Mean Distribution
- The sampling distribution of the sample mean should be normally distributed regardless of the population distribution, contradicting the idea that it can be skewed.
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Description
Test your knowledge with these flashcards covering key concepts from Statistics 122, Module 9. This includes topics such as the continuity correction in binomial distributions and the Central Limit Theorem. Perfect for students looking to reinforce their understanding of statistical theory.
