Question

Management of Melodic Kortholt Company compared absenteeism rates in two plants on the third Monday in November. Of Plant A's 800 employees, 120 were absent. Of Plant B's 1200 employees, 144 were absent. MegaStat's results for a two-tailed test are shown belowManagement of Melodic Kortholt Company compared absenteeism rates in two plants on the third Monday in November. Of Plant A's 800 employees, 120 were absent. Of Plant B's 1200 employees, 144 were absent. MegaStat's results for a two-tailed test are shown below.p1 p20.15 0.12 p (as decimal)120/800 144/1200 p (as fraction)120. 144. X800 1200 n0.03 sample difference0.00 hypothesized difference0.01545 std. errorx.xx z.0522 p-value (two-tailed)The test statistic (shown as z = x.xx) is approximately:A. 2.022B. 1.960C. 1.942D. 1.645

Answer 1

Answer: C. 1.942

Explanation:

This is a test of 2 population proportions. The population proportion of the number of absent employees in plant A and plant B are p1 and p2 respectively.

From the information given,

p1 = 0.15

p2 = 0.12

n1 = 800

n2 = 1200

To determine the z score, we would first determine the pooled proportion.

The pooled proportion, pc is

pc = (x1 + x2)/(n1 + n2)

pc = (120 + 144)/(800 + 1200) = 0.132

1 - pc = 1 - 0.132 = 0.868

The formula for z score is

z = (p1 - p2)/√pc(1 - pc)(1/n1 + 1/n2)

z = (0.15 - 0.12)/√(0.132)(0.868)(1/800 + 1/1200) = - 0.03/0.045

z = 1.942