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  • #4382 Balas
    HR Tiar
    Tamu

    Two machines used in the same operation are to be compared. A random sample of 80 parts from the first machine yields 6 nonconforming ones. A random sample of 120 parts from the second machine shows 14 nonconforming ones.

    a) Can we conclude that there is a difference in the output of the machines? Use a level of significance of 0.01.

    b) Find a 95% confidence interval for the difference in the proportion of nonconforming parts between the two machines.

    #4404 Balas
    R-Stats
    Keymaster

    Diketahui \(\hat{p}_1=\frac{5}{80}=\frac{1}{20}\) dan \(\hat{p}_2=\frac{14}{120}=\frac{7}{60}.\) Untuk soal (a) hipotesis yang digunakan adalah \[\begin{aligned} \text{H}_0 &: p_2-p_1=0\\ \text{H}_1 &: p_2 – p_1 \neq 0 \end{aligned}\] Statistik ujinya adalah \[z=\sqrt{\frac{(\hat{p}_1-\hat{p}_2)-d_0}{\hat{p}(1-\hat{p})\left( \frac{1}{n_1} + \frac{1}{n_2}\right)}}\] dimana \[\hat{p}=\frac{x_1+x_2}{n_1+n_2}\]

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