Test whether the sample is from a batch of a string having a mean breaking strength of 15.6 pound and S.D. of 2.2 pounds.

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

Marks: 5M

Year: May 2014

n =50 ($\boldsymbol{\gt}$30 ,so it is large sample)} $$\boldsymbol{\alpha }\boldsymbol{=}\boldsymbol{14}.\boldsymbol{5}\boldsymbol{\ ,\ }\boldsymbol{\sigma }\boldsymbol{=}\boldsymbol{2}.\boldsymbol{2}$$

Step 1 :

Null hypothesis ($H_0):\ \mu =15.6\ (i.e.\ the\ sample\ belongs\ to\ the\ population)$

Alternative hypothesis : $\mu \neq 15.6\ (i.e.\ the\ sample\ does\ not\ belong\ to\ the\ population)$

(Two failed tests)

Step 2:

L.O.S = 5%

$\mathrm{\therefore }$ Critical value ($z_{\alpha })=19.6$

Step 3 :

Since the sample is large,

S.E. = $\sigma /\sqrt{n}=2.2/\sqrt{50}$ = 0.3111

Step 4 :

Test statistic : $$z_{cal} = 14.5 -- 15.6/0.3111 = -3.5355$$

Step 5 :

Decision : Since |$z_{cal}|\gt z_{\alpha }$ , $H_0\ $is rejected.

Thus sample is not from a batch having a mean breaking strength of 15.6 pound.