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N2022 P2 Q7

N2022 P2 Q7

8 marks
Past Year National Exams
Free

A large company is organised into \(4\) departments: Administration, Production, Marketing and Staffing.

  1. The company owner wishes to find out about the qualifications of the employees in Staffing, so she gives a questionnaire to all \(75\) employees in this department. She receives replies from \(53\) of these employees. Explain whether these \(53\) employees form a population or a sample.[1]
  2. The company owner also wishes to investigate the views of employees about the refreshment facilities but does not have time to ask every employee. Explain how she should carry out her investigation, and why she should do the investigation this way.[2]

The company operates with a system of Team Leaders. There are \(7\) Team Leaders in Administration, \(6\) in Production, \(4\) in Marketing and \(3\) in Staffing.

  1. Find the number of ways in which a working party of \(8\) Team Leaders can be formed so that there is at least one Team Leader from each of the \(4\) departments AND there are more Team Leaders from Administration in the working party from any other single department.[5]

Video Solution:

Default solution

  1. The \(53\) employees who responded do not represent the entire Staffing department (which has 75 employees) but rather a subset of it. Therefore, the \(53\) employees form a sample of the population (the \(75\) employees in the Staffing department).
  2. She needs to collect a random sample of employees, ensuring each employee has an equal chance of being selected independently of each other. She can achieve this by numbering the employees and using a random number generator to select the corresponding employees. This method helps avoid bias and provides a representative sample.
  3. List item image
Answer:(a) The \(53\) respondents form a sample of the \(75\) Staffing employees. (b) Select a simple random sample from all employees so that every employee has an equal chance of selection. This reduces selection bias and gives a representative sample. (c) \(33642\)

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