Hypothesis Tests (t test, z test)

t distribution

A t distribution is also known as the student's t distribution and is used to make inferences about a mean when the standard deviation is unknown. 

The t distribution ranges from negative infinity to infinity and it a theoretical probability distribution. The higher the degrees of freedom, the closer that distribution will resemble a standard normal distribution with a mean of 0, and a standard deviation of 1. 

t-value

What is a t value?

t tests

There are a few different types of t tests: 1 sample t test, 2 sample t test, paired t test, and t test in regression output. 

Formula

 t =  x¯−μsN√

Assumption for using a t test

1. the population standard deviation is unknown
2. n < 30 (sample size less than 30)
3. the sample is drawn from a normal population

t distribution table

We find the t table value at α level of significance and n –1 degrees of freedom. If the calculated value is less than the critical value, then we accept the null hypothesis that the population mean and the sample mean are equal. Otherwise we reject the null hypothesis and conclude that the population mean and the sample mean are not equal.

z-value

What is a z value?

z test

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Assumptions for using a z test

1. when n > 30
2. when the distribution is normal