Question 1

Suppose you want to conduct a survey of benet packages available in private businesses in greater Melbourne. You have a directory of businesses that lists companies alphabetically. The directory lists the name of the business? suburb? and number of employees of 25m businesses The businesses are equally distributed across 25!] suburbs; each suburb has 1|] listed businesses. Among the 2500 listed businesses, can have less or equal to 10 employees. 35!] have 11-25 employees, 55H have 26-53 employees... 950 have 51-1l][l employee1 and 45!] have more than ll] employee. A snapshot of a section of the directory looks as follows. Company Name Suburb Number of Employees 2020 Global Business Melbourne less or equal to 10 Abbott Business Port Melbourne 11-25 ABC Business Hawthorn more than 100 Ace Business Carlton less or equal to 10 Active Business St Kilda 51-100 Ada Business South Yarra 26-50 Advantage Business Southbank more than 100 Ahrens Business St Kilda 11-25 All Business South Yarra less or equal to 10 Accredited Business Sydney 26-50 Atkins & Race Business Docklands 26-50 Baker Farlow Business St Kilda more than 100 Betta Business South Yarra 51-100 Better Business Richmond 26-50 1. Describe how to use stratified sampling to obtain a sample of 50. Specify which variable (suburb or number of employee) you would choose for stratification and why you choose this variable, compute the number of businesses you should select from each stratum using propor- tional sampling, and discuss how to obtain the sample. 2. Describe how to use cluster sampling to obtain a sample of 50. Specify which variable (suburb or number of employee) you would choose to form clusters, why you choose this variable, and how to obtain a sample of 50 using single stage sampling