Mumbai University > COMPS > Sem 4 > Applied Mathematics 4

Marks : 04

Year : MAY 2015

$n = 50$ (\gt 30, so it is large sample) $$\overline x=6.2 ; \sigma =10.24$$

Step 1:

Null hypothesis $(H_0): µ = 5.4$ (i.e sample belongs to the population with mean 5.4)

Alternative Hypothesis $(H_a): µ = != 5.4$ (i.e sample does not belong to population with mean 5.4) (Two tailed test)

Step 2:

LOS = 5% (Two tailed test)

Critical value $(z_x) = 1.96$

Step 3:

Since sample is large

$S.E=\dfrac {\sigma}{\sqrt n}=\dfrac {10.24}{\sqrt{50}} = 1.4482$

Step 4: Test statistic

$z_{cal} =\dfrac {\overline x- \mu}{S.E}=\dfrac {6.2-5.4}{1.4482}=0.5524$

Step 5: Decision

Since $Z_{cal} \lt Z_x, H_0$ is accepted.

Samples can be regarded as drawn from a normal population with mean 5.4 at 5% LOS.