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You must use the t-distribution table when working problems when the population standard deviation (σ) is not known and the sample size is small (n<30). General Correct Rule: If σ is not known, then using t-distribution is correct. If σ is known, then using the normal distribution is correct.
What is t-distribution and normal distribution ?
Normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.
In graphical form, the normal distribution appears as a "bell curve".
The normal distribution is the proper term for a probability bell curve.
In a normal distribution the mean is zero and the standard deviation is1. It has zero skew and a kurtosis of 3.
Normal distributions are symmetrical, but not all symmetrical distributions are normal.
The t-distribution describes the standardized distances of sample means to the population mean when the population standard deviation is not known, and the observations come from a normally distributed population.
Therefore,
You must use the t-distribution table when working problems when the population standard deviation (σ) is not known and the sample size is small (n<30). General Correct Rule: If σ is not known, then using t-distribution is correct. If σ is known, then using the normal distribution is correct.
Learn more about t-distribution and normal distribution here ;
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