1. Finding p-value (z-distribution & t-distribution)
EQT 271 Engineering Statistics
Maz Jamilah Masnan

2. Definition 2.6: p-value The p-value is the smallest significance level at which the null hypothesis is rejected.

3. Example 2.13 (One-Tailed Test)
When working properly, a machine that is used to make chips for calculators
does not produce more than 4% defective chips. Whenever the machine
produces more than 4% defective chips it needs an adjustment. To check if
the machine is working properly, the quality control department at the
company often takes sample of chips and inspects them to determine if the
chips are good or defective. One such random sample of 200 chips taken
recently from the production line contained 14 defective chips. Test at the 5%
significance level whether or not the machine needs an adjustment.

4. 1.65
0.95
Solution
2.17

5. P-value
= 0.5 – 0.485
=0.015

6. 1.65
0.95
Solution
P-value=0.015
2.17

7. Example 2.12 (Two-Tailed Test)

8. Solution
-1.96
1.96
1.84

9. P-value
= 0.5 –
=0.0329

10. -1.96
1.96
-1.96
1.96
1.84
P-value=2(0.0329)=0.0658

11. Finding p-value using t-distribution One-tailed-test

13. Since p-value is between 0.01 and 0.025 which is LESS THAN
=> Reject

14. Finding p-value using t-distribution Two-tailed-test

16. Since p-value is between 0.02 and 0.05 which is LESS THAN
=> Reject