Question

Michael is a delivery man for a pizza chain. He has 14 late deliveries out of 45 on

Sunday. The manager’s policy requires him to fire a delivery man if his rate of late

deliveries is above 0.2. Conduct a test at the 5% level of significance to determine if the

manager will fire Michael.

Answer 1

One sample proportion test used

$H_0 : P=0.2 \\ H_1: P > 0.2$

upper tail test

$p=\frac{14}{45} = 0.3333 \\ z = \frac{p – P}{\sqrt{P(1-P)/n}} \\ z = \frac{0.3333 -0.2}{\sqrt{0.2(1-0.2)/45}} \\ z=2.1602$

Table value of z at 0.05 level = 1.645

Rejection region: reject H₀ if z > 1.645

Calculated z = 2.1602 falls in the rejection region.

The null hypothesis is rejected. The manager will fire Michael.