Question

Explain the assumptions for using a two-independent sample t test. Provide an example for when you could use a a One-Sample t test. Provide an example for when a Two-Sample t Test.

Answer 1

The assumptions for using a two-independent sample t test are following :

1) The data measured on continuous scale.

Explanation: Because discrete data can never met normality assumption. But we can apply for discrete data because t-test is robust to this.

2) The data must be or approximately normally distributed.

Explanation: Because this test is designed for normally distributed data.

3) The two samples must be  independent to each other.

Explanation: If two samples are Not independent then we will get error in our result. We have different t test for paired data.

4) Both the samples must be random.

Explanation: Sample must be random because so that there will not be any biased error.

5) Populations standard deviations from which data are drawn must be unknown.

Example where we can use one sample t test:Suppose we know that average weight of 12 years old boy is 45 KG. We sampled 25 students randomly and calculated sample mean 47kg and sample standard deviation 9Kg. Now we want to test that the  average weight of 12 years old boy is different than 45 KG.

One sample t test use where we know population mean and we want to compare it with random sample mean and want to draw the conclusion.

Example for when a Two-Sample t Test. Suppose your class teacher always says that girls perform better than boys in test. To test this you randomly sampled 15 girls and 15 boys of your school and note their mean and standard deviation. .So in this case you will use two sample t test.