Question $1$

$[25]$

Work sampling is a statistical technique for determining the proportions of time spent by subjects in various defined activity categories. The manager of Jules Steel $($Pty$)$ Lad suspects that several workers are spending too much time waiting for materials during the cutting process. You have been tasked with conducting a work sampling study to quantify the percentage of idle time.

You conducted a preliminary study over one shift and made $150$ random observations, recording that the workers were idle during $30$ of these observations.

$1\mathrm{.}1$ Calculate the observed percentage of idle time and working time. Show all steps.

$1\mathrm{.}2$ Calculate $($based on $1,1)$ the number of observations needed to achieve an accuracy of $15\%$ at a $95\%$ confidence level. Use the formula provided in your study material.

$1\mathrm{.}3$ Discuss two potential causes for the high idle time in this type of environment and propose one realistic solution for each cause. Link your answer to the South Alrican manufacturing context.

$(8)$

$1\mathrm{.}4$ Briefly explain the key steps you would follow to complete the work sampling study and report the findings to management. Emphasise the importance of communication with workers during the study.