Question

A company's records indicate that on any given day about \(1 \%\) of their day- shift employees and \(2 \%\) of the night-shift employees will miss work. Sixty percent of the employees work the day shift. a) Is absenteeism independent of shift worked? Explain. b) What percent of employees are absent on any given day?

Short answer

a) No, absenteeism is not independent of shift worked. b) 1.4% employees are absent on any day.

Step-by-step solution

Determine overall absence probability

To determine if absenteeism is independent of the shift worked, calculate the total probability of absence regardless of shift. We do this by weighing each shift's absence probability by the proportion of employees working that shift.Calculate the probability that an employee is absent:For day shift: \[ P( ext{Absent} | ext{Day shift}) = 1 ext{ extperthousand} \] (or 0.01)For night shift: \[ P( ext{Absent} | ext{Night shift}) = 2 ext{ extperthousand} \] (or 0.02)The probability that an employee works the day shift is 0.60, hence the probability of absence is:\[ P( ext{Absent}) = (0.60 \times 0.01) + (0.40 \times 0.02) \]

Check for independence by comparing probabilities

To determine if absenteeism is independent of the shift, check to see if the probability of being absent is the same regardless of the shift worked.For absenteeism to be independent, we require:\[ P( ext{Absent} | ext{Day shift}) = P( ext{Absent}) \] and \[ P( ext{Absent} | ext{Night shift}) = P( ext{Absent}) \]Calculate \( P( ext{Absent}) \) using the formula from step 1:\[ P( ext{Absent}) = (0.60 \times 0.01) + (0.40 \times 0.02) = 0.006 + 0.008 = 0.014 \] (or 1.4%)Since \( 0.01 eq 0.014 \) and \( 0.02 eq 0.014 \), absenteeism is not independent of shift worked.

Calculate total percentage of absent employees

The total percentage of employees that are absent on any given day is already calculated as overall probability:Convert the probability to percent:\[ P( ext{Absent}) = 0.014 \times 100 = 1.4 ext{ extperthousand} \] Thus, 1.4% of employees are absent on any given day.

Key concepts

Absenteeism Analysis

Absenteeism analysis is a crucial measure for understanding patterns of employee absences. It helps in identifying factors that contribute to staff not attending work and their frequency. This allows companies to address potential issues and improve workplace efficiency. In this particular exercise, we look at absenteeism concerning day and night shifts.
By analyzing the exercise, we see that each shift has a different absenteeism probability:

• Day Shift: 1% absence rate
• Night Shift: 2% absence rate

This differing rate of absenteeism between shifts suggests that there are factors at play affecting employees' likelihood to miss work depending on their shift. This calls for a deeper investigation into why night shift absenteeism is higher, whether it’s due to scheduling, workload, or other social and health factors. Understanding these trends is key to creating supportive work environments and policies.

Conditional Probability

Conditional probability is the probability of an event occurring given that another event has already occurred. In the context of this exercise, it helps us understand the likelihood of employee absence given the shift they work.
Here are the formulas:

• \( P(\text{Absent | Day shift}) = 0.01\)
• \(P(\text{Absent | Night shift}) = 0.02\)

The concept helps us compare these probabilities to the overall absenteeism probability of 1.4% and determine if absenteeism depends on the shift worked. By calculating the overall absenteeism rate and comparing it to the conditional probabilities, it is evident that there is a dependence between absenteeism and the shift. If absenteeism was independent, the probability of being absent would be the same for the day and night shift, matching the overall absent rate, which is not the case here.

Shift Work Statistics

Shift work statistics provide valuable insight into how working on different shifts influences employee behavior and outcomes, such as absenteeism. In our exercise, 60% of employees are on the day shift, while the remaining 40% are on the night shift.
Here’s the breakdown:

• Day shift works with a 1% absentee rate.
• Night shift works with a 2% absentee rate.

With this information, we can weigh the absenteeism rate by the percentage of employees in each shift to find the overall absenteeism rate:\[P(\text{Absent}) = (0.60 \times 0.01) + (0.40 \times 0.02) = 0.014\]This means 1.4% of employees are absent on any given day. Understanding these statistics allows businesses to make informed decisions on scheduling, employee support systems, and balancing workloads between shifts. It can contribute to developing strategies that mitigate absenteeism and enhance employee satisfaction.