Question

In a sample of 50 turnings from an automatic lathe 8 were found to be outside specifications. The cutting

bits were then changed and the machine restarted. A new sample of 50 contained 3 defective turnings.

Find a 90% confidence interval for the decrease in the proportion defective after changing bits.

Answer 1

$Z_{\alpha/2}(90 \%)=1.645$

decrease in the proportion defective after changing bits is 8-3=5

$\mu=5 \plusmn(Z_{\alpha/2} \sigma)/ \sqrt{n}=5 \plusmn (1.645*0.1)/ \sqrt{50}=5 \plusmn 0.02$