Example 1: From a random sample of 576 of a company’s employees, it was found that the average number of days each person was absent from work due to illness was 8 days per annum, with a standard deviation of 3.6 days. What are the confidence limits for the average number of days’ absence through sickness per employee for the company as a whole - (a) at 95% level of confidence and (b) at a 99% level of confidence.

Outline of Answer s.e.= 8 1.96(0.15) 8 2.58(0.15)

Example 2 : In a random sample of 500 employees, 320 were members of a trade union. Estimate the proportion of trade union members in the entire organization at the 95% confidence level.

Outline of Answer P=320/500=0.64 N=500 s.e.= 0.64 1.96(0.0215) 0.64 1.96(0.0215) =60% to 68%

Example 3 : The management of a company making a certain type of car component wish to ascertain the average number of components per hour produced by the workers. Based on the previous sample, it is estimated that the average number produced by each employee every hour is 100, with a standard deviation of 25. The management now wish to know the true average to within ± 2 units. What must be the sample size if they want to be : (a) 95% certain (b) 99% certain?

Outline of Answer a) z=1.96; σ=25; d=2 n= b) As in (a), with z=2.58

Example 4: A manufacturer wishes to estimate the proportion of defective components. He would be satisfied if he obtained an estimate within 0.5% of the true proportion, and was 99% confident of his result. An initial large sample indicated that p = 0.02. What is the size of the sample he should examine?

Outline of Answer P=0.02; q=0.98; d=0.5%=0.005 n=