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Questions and Answers
Which theorem is critical to note if the distribution is non-normal and the sample size is low?
Which theorem is critical to note if the distribution is non-normal and the sample size is low?
- Law of Large Numbers
- Central Limit Theorem (correct)
- Chebyshev's Inequality
- Bayes' Theorem
What is the requirement for the Central Limit Theorem to apply?
What is the requirement for the Central Limit Theorem to apply?
- Non-normal distribution or sample size above 30
- Normally distributed population and sample size above 30
- Normally distributed population or sample size above 30 (correct)
- Non-normal distribution and sample size above 30
Which distribution is similar to the normal distribution and can be thought of as its 'brother'?
Which distribution is similar to the normal distribution and can be thought of as its 'brother'?
- Z distribution
- T distribution (correct)
- Poisson distribution
- Binomial distribution
What is the purpose of using the T distribution instead of the Z distribution?
What is the purpose of using the T distribution instead of the Z distribution?
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Which theorem is used to construct confidence intervals?
Which theorem is used to construct confidence intervals?
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Study Notes
Non-Normal Distributions and Small Sample Sizes
- The Tchebysheff Theorem is critical to note if the distribution is non-normal and the sample size is low.
Central Limit Theorem
- The requirement for the Central Limit Theorem to apply is that the sample size must be sufficiently large.
Normal Distribution Relatives
- The Logistic Distribution is similar to the normal distribution and can be thought of as its 'brother'.
T and Z Distributions
- The T distribution is used instead of the Z distribution when the population standard deviation is unknown and the sample size is small.
- The T distribution is more conservative and has a larger variance than the Z distribution.
Confidence Intervals
- The Central Limit Theorem is used to construct confidence intervals.
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Description
Test your understanding of the Central Limit Theorem and its application in constructing confidence intervals. Explore the conditions for the theorem to hold and learn when to use Z or T statistics.
