A company conduct a work sampling study to estimates the proportion of time thei

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.

Times busy

Times idle

Total observations

(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

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

Explanation / Answer

(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

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