7.4 Finite Population Correction Factor
The following activities and questions relate to material covered in Chapter 7.4 Finite Population Correction Factor in Introductory Business Statistics (OpenStax).
Data sets for the following questions are available in Excel: 7.4 Data Sets [XLSX].
Questions
- A local territorial brewery would like to know if the morning shift and the afternoon shift are equally efficient at brewing beer. The average brewing time is normally distributed with a mean of 2.38 hours days and a standard deviation of 0.36 hours. A study is completed to sample 10 shifts from the morning, and 13 shifts from the afternoon. The data was collected as below:
Shift Number of Hours to Process 100 Bottles of Beer Morning 2 Morning 2.2 Morning 2.3 Morning 2 Morning 3 Morning 2.6 Morning 2.2 Morning 2.6 Morning 2 Morning 2.6 Shift Number of Hours to Process 100 Bottles of Beer Afternoon 2.4 Afternoon 2.4 Afternoon 2.1 Afternoon 2.8 Afternoon 3.4 Afternoon 2.2 Afternoon 2.4 Afternoon 2 Afternoon 2 Afternoon 2.8 Afternoon 2.2 Afternoon 2 Afternoon 2.6 Complete the chart below and write a sentence to assess whether the morning or afternoon shift is more efficient at brewing beer.
Shift Sample Size Average Number of Hours to Process 100 Bottles of Beer Sample Standard Deviation z-score Morning Shift Afternoon Shift
Solutions
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Shift Sample Size Average Number of Hours to Process 100 Bottles of Beer Sample Standard Deviation z-score Morning Shift 10 2.35 0.34 0.28 Afternoon Shift 13 2.41 0.41 −0.24 Because the afternoon shift has a negative z-score (meaning they take less than the average time), the afternoon shift is more efficient at brewing beer compared to the morning shift.
