5 Questions
Which theorem is critical to note if the distribution is non-normal and the sample size is low?
Central Limit Theorem
What is the requirement for the Central Limit Theorem to apply?
Normally distributed population or sample size above 30
Which distribution is similar to the normal distribution and can be thought of as its 'brother'?
T distribution
What is the purpose of using the T distribution instead of the Z distribution?
To account for small sample sizes
Which theorem is used to construct confidence intervals?
Central Limit Theorem
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.
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.
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