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Can it be concluded that average life span of an Indian is more than 70 years ,if a random sample of 100 indians has an average life span of 71.8 years with standard deviation of 7.8 years.
$\text{(i) The null hypothesis H$_0$: μ = 70. Alternative hypothesis H$_1$: μ ≠ 70} \\$ $\text{(ii) Calculation of test statistic: Since sample size is large; Z =$\frac{(\bar{X} -μ)}{(\frac{σ}{\sqrt{n}})}$=$\frac{(71.8-70)}{(\frac{7.8}{\sqrt{100}})}$= 2.31} \$ $\text{(iii) Level of significance : α =0.05} \$ $\text{(iv) Critical value : the value of Z$_α$at 5% level of significance = 1.96} \$ $\text{(v) Decision : since the calculated value of |Z| =2.31 is greater than the table value Z$_α$=1.96. The null hypothesis is rejected} \$