Question

Assembly workers at Coastal Computers Inc. assemble just one or two subassemblies and insert them in a frame. The executives at CC think that the employees would have more pride in their work if they assembled all of the subassemblies and tested the complete computer. A sample of 26 employees was selected to experiment with the idea. After a training program, each was asked his or her preference. Twenty one liked assembling the entire unit and testing it. At the 0.010 level, can we conclude the employees preferred assembling the entire unit? (Round your answer to 2 decimal places.) He: AS 0.50 H11 > 0.50 Reject Hy if z > 2.33 z = 2.55 Reject HO: Workers prefer to assemble entire computer.

Answer 1

H: < 0.50

$H_1: \pi > 0.50$

n = 26,

p = (No. of people who prefer assembling the entire unit in a sample)/(Total number of employees in a sample)

   = (21/26)

   = 0.81

We'll do a Z-test for proportion. The value of the test statistic will be calculated as:

$Z = \frac{(p - \pi)}{\sqrt{\bigg[\frac{\pi(1-\pi)}{n}\bigg]}}$

  $= \frac{(0.81 - 0.5)}{\sqrt{\bigg[\frac{0.5(1-0.5)}{26}\bigg]}}$

(0.31) 0.5+0.5- 26

$= \frac{(0.31)}{0.098058}$

z = 3.16

Since, the calculated value of z(3.16) > the critcal value of z(2.33) at 0.01 significance level, we reject H0(which states that workers don't prefer assembling the entire unit). So, we can conclude that workers prefer assembling the entire unit.

Ans. Reject, don't prefer