Understanding The Concepts of Test of Hypotheses
Storyboard Text
- Hello, class! This is Ms. Villanueva and for today's lesson, we are going to tackle some key concepts of tests of hypotheses.
- What are we going to use, Ma'am?
- First, we need to determine the appropriate tool when the variance is known.
- A Z-test is used for the mean of the population when n ≥ 30, or when a population is normally distributed and the variance is known.
- Excuse me, Ma'am. What if the variance is unknown? Should we use the same one?
- No, Mr. Bart. This time, a T-test is used for the mean of a population when n < 30, or when a population is normally distributed and the variance is unknown.
- Said another way, CLT is a statistical theory stating that given a sufficiently large sample size from a population with a finite level of variance, the mean of all samples from the same population will be approximately equal to the mean of the population.
- Listen carefully. The Central Limit Theorem states that if the sample size is sufficiently large, then the mean of the random sample from a population has a sampling distribution that is approximately normal, even when the original population is not normally distributed
- After the class discussion...
- Hello! Can I ask? I forgot the lesson earlier
- I'm a bit confused on how too
- In simpler terms, the Z-test is used if the variance is known while we use the T-test if the variance is unknown. Also, sample sizes equal to or greater than 30 are considered sufficient for the Central Limit Theorem to hold.
- Now, I know how to determine the appropriate tools
- By knowing how to use the Central Limit Theorem, it allows us to safely assume that the sampling distribution of the mean will be normal in most cases.
- That's correct! We also don't need to memorize what we have learned, we just have to understand the concepts and apply them in the future.
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