Question

When producing a workpiece, the reject rate is questioned. A random sample of n = 100 pieces is now randomly taken from the current production. The sample is 98 perfect pieces. Determine the 90% confidence interval for the population share.

Answer 1

Solution :

n = 100

x = 98

= x / n = 98 / 100 = 0.980

1 - = 1 - 0.980 = 0.020

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z_0.05 = 1.645

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 1.645 * (((0.980 *0.020) / 100)

= 0.023

A 90 % confidence interval for population proportion p is ,

- E < P < + E

0.980 - 0.023 < p < 0.980 + 0.023

0.957 < p < 1.003