A researcher in a large organization wishes to study sickness absence amongst its employees. The organization has a large number of branches, each of each keeps full records of sickness leave. A random sample of 10 such branches produced the following data showing the number of sickness per branch in past one year. 18 23 26 30 32 35 39 45 48 54 Required: a) Using the data i) Calculate a 95% confidence interval for the mean mount of sickness days per branch. ii) Estimate the number of branches that should be included in a simple random sample so that 95% confidence interval for the mean number of days of sickness should not have a width greater than four days. b) After the sample was collected, it became apparent that the branches fell into three natural groups in terms of sales – small, medium and large. From her data on all the branches, the researcher found that 210 randomly selected staff, 90 worked in small branches, 36 in medium-sized branches and the rest worked in large branches. In total, 96 of the selected staff had no days off for sickness, of which 52 worked in small branches and 29 worked in large-sized branches. i) Form a table showing this information clearly ii) Carry out an appropriate statistical test to investigate whether the size branch influences the occurrence of sickness absence and interpret your results
A researcher in a large organization wishes to study sickness absence amongst its employees. The organization has a large number of branches, each of each keeps full records of sickness leave. A random sample of 10 such branches produced the following data showing the number of sickness per branch in past one year.
18 23 26 30 32 35 39 45 48 54
Required:
a) Using the data
i) Calculate a 95% confidence interval for the mean mount of sickness days per branch.
ii) Estimate the number of branches that should be included in a simple random sample so that 95% confidence interval for the mean number of days of sickness should not have a width greater than four days.
b) After the sample was collected, it became apparent that the branches fell into three natural groups in terms of sales – small, medium and large. From her data on all the branches, the researcher found that 210 randomly selected staff, 90 worked in small branches, 36 in medium-sized branches and the rest worked in large branches. In total, 96 of the selected staff had no days off for sickness, of which 52 worked in small branches and 29 worked in large-sized branches.
i) Form a table showing this information clearly
ii) Carry out an appropriate statistical test to investigate whether the size branch influences the occurrence of sickness absence and interpret your results
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