The hypothesis which is accepted when the null hypothesis has been rejected is called the alternative hypothesis. It is denoted by or . Whatever we are expecting from the sample data is taken as the alternate hypothesis. For example, stating “More than 25% people are literate in our country” means we are hoping to get this result from the sample. It will be taken as an alternate hypothesis and the null hypothesis will be that 25% or less are literate. To be more specific, will be 25% or less are literate and will be more than 25% are literate. It is written as:
(25 % or less) (More than 25 %)
To keep the things simple, we can write H0 in the form of equality as
but it is important to write H1 with the proper direction of inequality. Thus we write .
In this case the contains the inequality of more than (>). We shall explain later that may be written with the inequality less than (<) or not equal (). In general, if the hypothesis about the population parameter 8 is 00, then H can be written in three different ways.
This is the simple approach, which is allowed for students. Another way of writing the above hypotheses and is
The alternative hypothesis never contains the sign of equality. Thus will not contain ‘=‘, ‘‘or ‘‘signs. The equality sign ‘=‘and inequalities like ‘ ‘and ‘‘are used for writing .