Question

The CEO of a mail order business is reviewing the order filling operations at their two warehouses. The goal is to have 100% of orders shipped within 24 hours. In previous years, neither warehouse has achieved the goal, but the East Coast Warehouse has consistently out-performed the West Coast Warehouse.
To compare the current performance of the warehouses, they decide to conduct a hypothesis test at the 5% significance level. They randomly select 200 orders from the West Coast Warehouse (population 1) and 180 orders from the East Coast Warehouse (population 2). They found that 178 of the West Coast Orders were shipped within 24 hours, and the East Coast Warehouse shipped 165 orders within 24 hours. What is the p-value for testing the hypothesis whether there is a difference in the proportion of shipments at the two warehouses ?

Answer 1

n1 = Size of Sample 1 = 200

p1 = Proportion of Sample 1 = 178/200 = 0.89

n2 = Size of Sample 2 = 180

p2 = Proportion of Sample 2 = 165/180 = 0.9167

Q = 1 - P = 0.0974

Test statistic is given by:
Z = (0.89 - 0.9167)/0.0305 = - 0.8764

Table of Area Under Standard Normal Curve gives = 0.3106

So,

P- Value = (0.5 - 0.3106) X 2 = 0.3788

So,

Answer is:
p - value is given by:

0.3788