Question

One way to write the research hypothesis for the independent-measures t-test is:

Answer 1

The independent samples t test (also called the unpaired samples t test) is the most common form of the T test. It helps you to compare the means of two sets of data. For example, you could run a t test to see if the average test scores of males and females are different; the test answers the question, “Could these differences have occurred by random chance?”

Assumption of Independence: you need two independent, categorical groups that represent your independent variable. In the above example of test scores “males” or “females” would be your independent variable.
Assumption of normality: the dependent variable should be approximately normally distributed. The dependent variable should also be measured on a continuous scale. In the above example on average test scores, the “test score” would be the dependent variable.
Assumption of Homogeneity of Variance: The variances of the dependent variable should be equal.

If M1 and M2 be the true population means for two independent groups of variables,

to test, H0:Means are equal or

H0:M1=M2

vs

H11:Means are unequal

H11:M1M2

or H12:Mean of 1st population is less than that of 2nd population.

ie H12:M1<M2

or H13:Mean of the 1st population is greater than that of 2nd population.

or H13:M1>M2.

If there is any understanding problem regarding this please feel free to ask any doubt in comment box. Thanks.