Question

what is required to use a T test, and what is different in the requirements from using a Z test

Answer 1

Requirement to use t-test :

Main assumption is when population standard deviation or population variance unknown

then we can estimate sample mean and sample standard deviation s

The one sample t-test has four main assumptions:

• The dependent variable must be continuous (interval/ratio).
• The observations are independent of one another.
• The dependent variable should be approximately normally distributed.
• The dependent variable should not contain any outliers.

The paired sample t-test has four main assumptions:

• The dependent variable must be continuous (interval/ratio).
• The observations are independent of one another.
• The dependent variable should be approximately normally distributed.
• The dependent variable should not contain any outliers

Now,

Requirement to use z-test

Main assumption is when population standard deviation or population variance known

You would use a Z test if:

• Your sample size is greater than 30. ...
• Data points should be independent from each other. ...
• Your data should be normally distributed. ...
• Your data should be randomly selected from a population, where each item has an equal chance of being selected.
• Sample sizes should be equal if at all possible.

Same for two population mean test

For proportion test we always use Z-test.

because, Population proportion ~