Question

1-Give an example of a null hypothesis and alternate (research) hypothesis that might be a good use of a t-test for independent samples.

Answer 1

Solution: A t-test is used to test whether two populations ( independent) have different average values and one example is given below:

Scenario : We want to check if the income of Americans( call it population X) and English( call it population Y) people  is different or not

So here , we can collect a sample of incomes from both USA and England and calculate their average( collecting income from population is tough).

Generally the average income would be supposed to reflect the income of population

Ux=Mean income of Americans

Uy=Mean income of English

So hypothesis would be

NULL HYPOTHESIS H₀: Average Income of American =Average Income of British i.e. Ux =Uy

ALTERNATIVE HYPOTHESIS:   H₁: Average Income of American    Average Income of British i.e. Ux Uy

Alternative hypothesis can be others also , like UxUy or Ux<Uy

Taking a sample of suitable size and using the test statistics we can arrive on conclusion about the population using t_test.