How do I use t-distribution to estimate the tα/2

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SUMMARY

The discussion centers on using the t-distribution to estimate the tα/2 value for calculating confidence intervals in small sample sizes. The participants clarify that α represents the level of significance in hypothesis testing, indicating the probability of obtaining results due to chance. The problem involves finding the population mean and standard deviation, listing all possible samples of size 3 from a dataset of 5 units, and computing the mean, standard deviation, and 95% confidence interval for each sample using the t-distribution.

PREREQUISITES
  • Understanding of t-distribution and its application in statistics
  • Knowledge of confidence intervals and how to compute them
  • Familiarity with the concept of sample means and standard deviations
  • Basic grasp of hypothesis testing and significance levels (α)
NEXT STEPS
  • Study the properties and applications of the t-distribution in statistical analysis
  • Learn how to compute confidence intervals using the t-distribution
  • Explore the empirical rule and its relevance in probability distributions
  • Practice calculating sample means and standard deviations from datasets
USEFUL FOR

Statisticians, data analysts, students in statistics courses, and anyone involved in hypothesis testing and confidence interval estimation.

lilyungn
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Hi, I need help understanding how do I use t-distribution to estimate the tα/2 . Also what is meant when it asks "verify your result with empirical rule"
 
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Do you understand what α is?
 
no i dont, what is it?
 
It is the level of probability to be used for testing. The probability that the result is due to chance.

Do you know what a probability distribution is?
 
Basically I'm working on a problem that asks that part of the question. I have solved for the population mean, and have different samples with 3 data in them. I calculated the x-bar of those samples with the standard dev and have gotten their confidence intervals.
 
That's all very good; how does your original question about the t distribution relate to the rest?
 
here is the question:

- Find the population mean and its standard deviation
- List all possible samples of size 3 from those 5 units
- From each sample, compute the mean, standard deviation, and 95% confidence interval. Use t-distribution to estimate the tα/2 because we have a small size.
 
Questions like this belong in the Homework forum. Please post there next time. Hey, I don't make the rules around here.
 

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