Question

A total of 280 observations of Bob Ramos, an assembly-line worker, were made over a 40-hour work week. The sample also showed that Bob was busy working (assembling the parts) during 240 observations. (Round all intermediate calculations to at least two decimal places before proceeding with further calculations.)

a) a) The percent of time Bob is working = _______

b) The number of observations that need to be taken of Bob to be 95 % confident with 5 % acceptable error = _______

c) Was the sample size adequate?

Answer 1

a.Total observations made = 280

Number of observations where Bob was busy working= 240

The percent of time Bob is working based on the observation= (240/280)*100%= 85.71%

b. desired confidence level= 95%

Corresponding value of z= 1.96

Acceptable error, e= 5%= 0.05

Number of observations to be made, n= (z/e)²p(1-p)

p = sample proportion = 85.71%= .8571

Hence n= (1.96/0.05)²x0.8571(1-0.8571)= 188.21

Number of observations to be made = 188

c. The sample size was adequate as required number of observations(188) is less than the sample size(280).