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

Marks: 6M

Year: May 2015

n=100($\gt$30, so it is large sample) $$\overline{x_1}=71.8\ ;z=7.8$$

Step 1 :-

Null Hypothesis (H${}_{0}$)=$\mu$=70(i.e. the average life span of an Indian is 70 years)

Alternative Hypothesis(H${}_{x}$)=$\mu$$>$70(i.e. the average life span of an Indian is more than 70 years) (one tailed test)$\$

Step 2 :-

LOS=5% (Two tailed test)

LOS=10%(One tailed test)

$$\mathrm{\therefore } Critical value (z{}_{\mathrm{\infty}})=1.64$$ Step 3:- Since sample is large , $$S.E.=\frac{s}{\sqrt{n}}=\frac{7.8}{\sqrt{100}}=0.78$$ Step 4 :- Test statistic . $$t_{cal} =\frac{\overline{x}-\mu }{S.E.} =\frac{71.8-70}{0.78} =2.3077$$

Step 5 :- Decision

Since |teal|$\gt$t${}_{\mathrm{\propto }}$,H${}_{0}$ is rejected $\mathrm{\therefore }$ The average life span of an Indian is more than 70 years.