Question One

$[$Total marks:$20]$

The Human Resource Manager at a manufacturing plant noticed that there was a high rate of absenteeism$,$ lack of motivation, reduced cooperation and low productivity among the employees. She suspected that the employees' morale had decreased. The Human Resource Manager decided to select the first $100$ employees who arrived to work on a certain day and ask them to complete an employee morale survey. Each employee's level of morale was measured between $1$ to $15$ inclusive; with $15$ indicating the highest level of employee morale. The data was summarized in Table $1$ below.

TABLE $1$

$\backslash$table$[[$Level of Employee morale,Number of Employees$],[1-3,8],[4-6,26],[7-9,40],[10-12,18],[13-15,8]]$

a$)$ Identify the population for this investigation.

$[1]$

b$)$ Identify the sample for this investigation.

$[1]$

c$)$ Identify the sampling method that was used to select the sample. Give one advantage and one disadvantage of using this sampling method.

$[3]$

d$)$ For each of the following charts: stem$-$and$-$leaf diagram, box$-$and$-$whisker diagram, bar chart and histogram, indicate whether or not the chart would be suitable for presenting the data displayed in Table $1$ above. Give reason for your answer.

$[4]$

e$)$ Use Table $1$ to calculate:

i$.$ the mean employees' morale.

$[3]$

ii$.$ the median

$[4]$

iii. The mode

$[4]$

Question Two

$[$Total marks: $10]$

Recent graduates of the UWI Open Campus were randomly selected and surveyed to determine what programme they were enrolled in while they were a student. The data was inputted into MINITAB for analysis to determine whether programme of study is independent of gender. The following output, Exhibit $1,$ was generated using MINTAB

EXHIBIT $1$

Chi$-$Square Test for Association: Gender, Programme of Study

Rows: Gender Columns: Programme of Study

$\backslash$table$[[,\backslash$table$[[$Associate$],[$Degree$]],$Accounting,$\backslash$table$[[$Banking$],[$and$],[$Finance$]],\backslash$table$[[$Management$],[$Studies$]],$Other$],[$Female$,\backslash$table$[[******$