Question one

A researcher in a large supermarket wishes to study sicknessabsences among its employees. The
organisation has branches in all the provinces, each branch keepsfull records of sickness leave. A random sample of ten suchbranches produced the following data showing the number ofdays
of sickness per branch in the year 2017.
18 23 26 30 32 35 39 45 48 54
Required:
a) Using the above data

a). Calculate (manually and using the computer software such asEXCEL, SPSS etc), a
95% confidence interval for the mean amount of sickness days perbranch.

b). Estimate the number of branches that should be included in asimple random sample so that a 95% confidence interval for the meannumber of days sickness should not have a width greater than 4 days5 marks
c)) After the sample was collected, it became apparent that thebranches fell into three natural groups in terms of sales-small,medium and large. From the data on all of the branches in theprovinces, the researcher found that of 210 randomly selectedstaff, 90 worked in small branches, 36 in medium sized branches,and the rest worked in large branches. In total, 96 of the selectedstaff had no days off for sickness, of which 52 worked in smallbranches, and 29 worked in large sized branches.
i) Form a table showing the information clearly. 5 marks
ii) Carry out an appropriate statistical test to investigatewhether the size of branch influences the occurrence of sicknessabsence, interpret your results clearly.