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A machine is set to produce metal plates of thickness 1.5 cms with S.D. of 0.2 cms .

A machine is set to produce metal plates of thickness 1.5 cms with S.D. of 0.2 cms . A sample of 100 plates produced by the machine gave an average thickness of 1.52cms .Is the machine fulfilling the purpose?

$\text{(i) The null hypothesis H$_0$: μ = 1.5. Alternative hypothesis H$_1$: μ ≠ 1.5}$ $\text{(ii)Calculation of test statistic: Since sample size is large; Z =$\frac{(\bar{X} -μ)}{(\frac{σ}{\sqrt{n}})}$=$\frac{(1.52-1.5)}{(\frac{0.2}{\sqrt{100}})}$= 1}$ $\text{(iii) Level of significance : α =0.05}$ $\text{(iv) Critical value : the value of Z$_α$at 5% level of significance = 1.96}$ $\text{(v) Decision : since the calculated value of |Z| =1 is less than the table value Z$_α$=1.96. Therefore, the null hypothesis is accepted i.e. The machine fulfilling the purpose }$