Question

In a test to compare two population means which of the following alpha levels requires the least difference between the sample means in order to allow rejection of Ho : u1 = u2? (assume all factors are equal).

Answer 1

Alpha level is a probability which generally are 1%, 5% or 10% (can be something else as well)

When comparing two population means we can use normal or t-dist depending upon the available information.

Normal test

When the population SD is known we can use this distribution where the test stat is

Test Stat :

We find the probability p -value using

P-value = .....................Value found using normal tables.

If p-value < level of significance we reject the null hypothesis.

So the level of significance should be greater than p - value

Eg: p -value = 0.045

Then a level of significance > 0.045 will be taken for rejection

t-dist test

When the population SD is unknown and the 'n' is either large or we assume that the samples come from normal population we can use this t-distribution where the test stat is

Test Stat :

Where Pooled variance

We find the probability p -value using

P-value = .....................Value found using t-dist tables with x = T.S. df =

If p-value < level of significance we reject the null hypothesis.

So the level of significance should be greater than p - value

Eg: p -value = 0.045

Then a level of significance > 0.045 will be taken for rejection