Mumbai University > Mechanical Engineering > Sem 4 > Applied Mathematics IV

Marks: 5M

Year: Dec 2014

n = 900 ($\gt$30, so it a large sample) $$\overline{x} = 65.3 ; \sigma =5$$

Step 1 :

Null Hypothesis ($H_0)\ :\ \mu $ = 66.2 (the sample belongs to the population with mean 66.2)

Alternative hypothesis ($H_A)\ :\ \mu $ $\mathrm{\neq}$ 66.2 (the sample does not belong to the population with mean 66.2)

Step 2 :

L.O.S : 5%

Hence , Critical value ($z_{\propto }$) = 1.96

Step 3 :

Since the sample is large,

S.E. = $\sigma /\sqrt{n}$ = 5/$\sqrt{900}$ = 0.1667

Step 4 :

Test statistics : $$z_{cal}=\ \ \overline{x}-\ \mu /S.E. = (65.3-66.2)/0.1667 = -5.4$$

Step 5 :

Decision :

Since, $z_{cal}\gt z_{\propto }$ , $H_0$ is rejected.

$\boldsymbol{\mathrm{\therefore }}$ Sample does not belong to the population with mean 66.2