Question

how to recognize each of the following (in a study)
one-sample t  
2 independent sample t
related sample t  
one-sample z-test

Answer 1

We use different t-test when the sample size is less than 30, the population standard deviation is unknown and the following conditions are satisfied:

• The data were collected in a random way.
• Each observation must be independent of the others.
• The sampling distribution must be normal or approximately normal.

Now, to recognize which t-test is to use, we consult the table given below:

Test	Purpose	Example
1-sample t-test	To test whether the mean of a single normally distributed population is equal to a target value (or hypothesised value)	Is the mean height of female college students greater than 5.5 feet?
2-Sample t-test	To test whether the difference between the means of two independent normally distributed populations is equal.	Does the mean height of female college students significantly differ from the mean height of male college students?
Relate t-test or Paired t-test	To test whether the mean of the differences between dependent or paired observations is equal.	If you measure the weight of male college students before and after each subject takes a weight-loss pill, is the mean weight loss significant enough to conclude that the pill works?

One sample Z-test

We use Z-test when the data were collected in a random way, each observation must be independent of the others, the sampling distribution must be normal or approximately normal, and the population standard deviation must be known.

We use One sample Z-test to test the mean of a normally distributed population with known variance is equal to a target value.

For example, the manager of a candy manufacturer wants to know whether the mean weight of a batch of candy boxes is equal to the target value of 10 ounces.