$\text{(i) The null hypothesis H$_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$=1.96. Therefore, the null hypothesis is accepted
i.e. The machine fulfilling the purpose }$