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.
One sample proportion test used
"H_0 : P=0.2 \\\\\n\nH_1: P > 0.2"
upper tail test
"p=\\frac{14}{45} = 0.3333 \\\\\n\nz = \\frac{p \u2013 P}{\\sqrt{P(1-P)\/n}} \\\\\n\nz = \\frac{0.3333 -0.2}{\\sqrt{0.2(1-0.2)\/45}} \\\\\n\nz=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.
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