Diane Chen, the Human Resources Manager for a private college, is interested in examining the number of hours overtime worked by staff in one week. She took a sample of 6 staff, with the results given below.

2, 1, 4.5, 7, 8, 5

a) Is the number of hours overtime worked by staff in a week categorical or numerical variable. If the variable is numerical, determine whether the variable is discrete or continuous. In addition, determine the level of measurement (eg ratio or nominal scale).

b) Calculate the sample mean of this sample. Include units.

c) Calculate the sample standard deviation (correct to 3 decimal places). Include units.

d) What must be assumed about the population distribution in order to calculate a confidence interval? Give a reason for your answer

e) Using the sample mean and sample standard deviation (found in b and c) calculate the 90% confidence interval for the population mean overtime hours. Include a concluding statement.

f) If one staff member claimed they worked 7 hours overtime, based on this sample should you take their statement as true? Why/ why not?