When testing or the difference of means 1 – 2 from independent populations, how

Question

When testing or the difference of means 1 – 2 from independent populations, how do we decide whether to use the standard normal distribution or a Student's t distribution? If the x distribution is normal and n 30 with known we use the Student's t. With the same conditions and unknown we use the standard normal. If the x distribution is normal and n 20 with known we use the standard normal. With the same conditions and unknown we use the Student's t. Whenever we assume the populations are independent, we always use the standard normal. If the x distribution is normal and n 30 with known we use the standard normal. With the same conditions and unknown we use the Student's t.

Explanation / Answer

As the sample size (and thus the degrees of freedom) increases, the t distribution approaches the bell shape of the standard normal distribution. In practice, for tests involving the mean of a sample of size greater than 30, the normal distribution is usually applied.

Student’s t-test, in statistics, a method of testing hypotheses about the mean of a small sample drawn from a normally distributed population when the population standard deviation is unknown.

If the x distribution is normal and n 30 with known we use the standard normal.

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