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- TRISHA NADAL L. LAGUNERO#160;11 - STEMWEEK 4: STATISTICS PROBABILITY (WHAT I CAN DO)
- Identifying the Appropriate Tool when theVariance is known, Variance is unknown, and when Central Limit Theoremis used
- How should we determine the appropriate tool to be used in the test statistic?
- To identify the test statistic, you must consider whether thepopulation standard deviation/variance is known or unknown.
- Oh, I know what are those!
- If the population standard deviation σ is unknown,then the mean has a t- distribution. Use t-test.
- If thepopulation standard deviation σ is known, then the mean has a normaldistribution. Use z-test.
- In a z-test, the sample is assumed to be normally distributed. It#160;is calculated with population parameters. Thevariance is known and either the distribution is normal
- While in a t-test , it also assumes a normal distribution of thesample. A t-test is used when the population variance or standard deviationare not known.
- That's right!
- When thevariance is known and sample size isgreater than or equal to 30, use a z-test statistic. And when the variance is unknown and a sample size is lessthan 30, use a t-test statistic
- But what if the sample size is considered sufficiently large and the variance is known or unknown?
- We use z-test in this by replacingpopulation standarddeviation (σ) by samplestandard deviation (s) inthe formula.
- We have the Central Limit Theorem (CLT). It applies when population may not benormally distributed,#160;the variance is known or unknown,#160;and the sample size is considered sufficiently large
- Alright. Have a great day!
- That's it. I hope we both learned something from this discussion.
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