Chapter 4.1, Problem 17E

To determine

To describe how to select a stratified random sample of approximately thirty employees and explain your choice of strata and also explain why stratified random sampling might be preferred in this context.

Explanation of Solution

The owner of a large restaurant is considering a new “no tipping” policy and wants to survey a sample of employees. By doing this, we may add some percent of cost to the food and beverages and then distribute the additional revenue equally among the servers and kitchen staffs.

To select the stratified random sample, we need to first define the population i.e. the population we need to examine that is the servers and the kitchen staffs. And the sample of thirty employees that is to be taken from the population. Then secondly, we need to find the relevant stratification that is the strata that is to be taken for the survey. The strata are the groups from the sample that is taken for surveys. The strata in this case may be the groups of servers and the other one is kitchen staff. And we need to ensure that the number of units selected for the sample from each stratum is proportionate to the number of servers and kitchen staff in the population. This can be taken as $15$ servers and $15$ kitchen staffs employees can be taken into the sample and then our random stratified sample is selected.

Stratified random sampling is preferred in this context as the tips are given to the servers only the kitchen staff is left behind. Thus, in order to consider the kitchen staff employees also and their additional earning it is better to survey them separately to make sure that the sample of the survey is not biased.