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 =85.71

b) The number of observations that need to be taken of Bob to be 90 % confident with 5 % acceptable error = __

c) Was the sample size adequate?

Answer 1

To be calculated:

(a) Percent of time Bob is working

(b) Number of observations required or sample size (90% confidence, 5% acceptable error)

(c) If the sample size is adequate or not

Given Values:

Sample size, S = 280

Number of times Bob was found working = 240

Solution:

(a) Percent of time Bob is working can be calculated as;

Efficiency = (Number of times Bob was working / Sample size ) x 100

Efficiency = ( 240 / 280 ) x 100 = 0.8571 x 100 = 85.71%

(b) Number of observations required (Sample size, S) can be calculated as;

S = [(Z^2) x P x (1 - P)] / (E^2)

where,

Z = z-value,

P = percentage working

E = Acceptable error

Z (at 90% confidence) = 1.645

P = 0.857 or 0.86 (rounding off to two decimal places)

E (at 5% acceptable error) = 5 / 100 = 0.05

Therefore, S = [(1.645^2) x (0.86) x (0.14)] / (0.05^2)

S = 130.32 or 130 (rounding off to the nearest whole number)

S = 130

The number of observations that need to be taken of Bob to be 90% confident with 5% acceptable error = 130

(c) The current number of observations are 280 while the required number of observations are 130. Therefore, the current sample size is adequate.