Example A group of 200 students have the
mean height of 154 cms. Another group of 300 students have the mean
height of 152 cms. Can these be from the same population with S.D.
of 5 cms?
Solution: H_{o} : m_{1}
= m_{2}, the samples are from
the same population.
H_{a} : m_{1}
¹ m_{2}, here
= 154 cms,
= 152 cms, s = 5 cms, n_{1} = 200 and n_{2}
= 300.
Now,
i.e. the zscore is highly significant. Therefore, we reject H_{o} i.e. it is not likely that the two samples are from the same population.
Example Random samples from two population
gave the following results :

Population A 
Population B 
Mean 
490 
500 
S.D. 
50 
40 
Size 
300 
300

Is the difference between the means significant?
Solution: H_{o} : m_{1}
= m_{2},
the difference between the two means is not significant. i.e. H_{a}
: m_{1}
¹ m_{2}.
We have = 490, = 500, s_{1} = 50, s_{2} = 40, n_{1} = 300 and n_{2} = 300.
Therefore, the null hypothesis H_{o} is accepted i.e. the difference between the two means is not significant.
