Question

A company conduct a work sampling study to estimates the proportion of time their workers on idle during the process. The table below shows the data.

Observation Period	Times busy	Times idle	Total observations
Monday	6	1	7
Tuesday	5	2	7
Wednesday	7	0	7
Thursday	9	2	11
Friday	5	5	10
Total	32	10	42

(a) What is the estimated percentage of idle time?(answer 0.238

(b) Based on the initial results, approximately how many more observations would you require estimating the actual percentage of idle time to within 5% with a confidence of 98%? (Ans. 352 more observations)

Using the information in the following grid, determine if the department locations shown are appropriate. If not, modify the locations so that the conditions are satisfied

Answer 1

(a) Estimated percentage of idle time = 10/42 = 0.2380952 = 0.238

This is also called sample proportion, p = 0.238

(b) Required sample, n = (z/e)^2 * p * (1-p)

Here, z = No. of standard deviation for desired confidence level

For 98% confidence level, Z = 2.33

e = required error percentage limit = 5% = 0.05

p = 0.238

So, n = (2.33/0.05)^2 * 0.238 * (1 - 0.238)

=> n = 393.9338

=> n = 394

So, required sample size = 394.

So, additional observations required = 394 - 42 = 352