QUESTION

When working properly, a machine that is used to make a chips for calculators produce

4% defective chips. Whenever the machine produce more than 4% defective chips it

needs an adjustment. To check if the machine is working properly, the quality control

department in the company often takes sample of chips and inspects them to determine

if they are good and defective. One such random sample of 200 chips taken recently

from the production line contains 14 defective chips. Test at the 5% significance level

whether or not the machine needs an adjustment.

Solution:

P0 = 4 % = 0.04

1. The hypothesis to be tested are:

H0: P = 0.04

H1: P > 0.04

2. Test statistic

𝑍 =0.07 − 0.04

√0.04(1 − 0.04)200

Z = 2.17

3. Critical region: Z > z

z = z0.05 = 1.65

4. 2.17 > 1.65 falls the rejection region, H0 are reject.

5. Conclude the machine need an adjustment

QUESTION

When working properly, a machine that is used to make a chips for calculators produce

4% defective chips. Whenever the machine produce more than 4% defective chips it

needs an adjustment. To check if the machine is working properly, the quality control

department in the company often takes sample of chips and inspects them to determine

if they are good and defective. One such random sample of 200 chips taken recently

from the production line contains 14 defective chips. Test at the 5% significance level

whether or not the machine needs an adjustment.

Solution: