Answer to Question #187329 in Statistics and Probability for Khalilah Spencer

Question #187329

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.


1
Expert's answer
2021-05-07T10:41:03-0400

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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