z-test y-yesy central limit theorem
Storyboard Text
- Slide: 1
- While this knife is a Central Limit theorem, some pieces might be big, some small, but the more I chop, the more they average out to a uniform size.
- Oh! Central Limit Theorem is that no matter how the data looks at first, with at least 30 samples, the averages form a normal distribution!
- Exactly! Whether variance is known or unknown, we can still use the Z-test, replacing the population's standard deviation with the sample's in the formula.
- Slide: 2
- Now let's test your knowledge! A company claims their chocolate bars weigh exactly 50 grams. The standard deviation of their chocolate bars is known to be 5 grams. A food inspector randomly selects 100 bars and finds their average weight is 48 grams.
- The sample size is 100 and the population standard deviation known is 5 grams.
- Then the appropriate test statistic to to be used is Z-test.
- Slide: 3
- So samples help us understand populations, and different tests help us analyze them.
- And choosing the right test is like picking the right recipe—it makes all the difference!
- Great job, kids! Before anything else, let’s go over the key ingredients of statistics!A population includes all data points, while a sample is a smaller subset. The sample mean (x̄) estimates the population mean (μ), and when the sample is large and random, it provides a reliable estimate. The population standard deviation (σ) measures overall variability, while the sample standard deviation (s) estimates it from a subset. Population variance (σ²) shows data spread across the population. A test statistic is a value calculated from sample data to compare results with expectations under the null hypothesis in hypothesis testing.
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