Question

Two different types of injection- moulding machines are used to form plastic parts. A part is considered defective if it has excessive shrinkage or is discoloured. Two random samples, each of size 300, are selected, and 15 defective parts are found in the sample from machine 1, and 8 defective parts are found in the sample from machine 2. Is it reasonable to conclude that both machines produce the same fraction of defective parts, using a 0.05, find the value of Zcalc: Please report your answer upto 2 decimal places.

Answer 1

let n=300 each and x1=15 and X2=8

The hypotheses are:

Ho: P1=P2'

Ha: P1$\neq$P2

Rejection region:

at 0.05 level of significance reject Ho if |Z_obs|>Z_0.0025=1.96

Test statistic:

(P1 -P2) -0 ni n2

Where, $\hat{P}_{1}=\frac{X1}{n}$ and$\hat{P}_{2}=\frac{X2}{n}$

$\hat{P}=\frac{X1+X2}{n+n}$

Z(Calc)=1.49

Conclusion:

Since Z<Z_0.05 hence we fail to reject the null hypothesis and conclude that there is insufficient evidence to say that the proportion differs, hence it is reasonable to conclude that both machines produce the same proportion of defect.