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The analyst in the Dorben Reference Library decides to use the work sampling technique to establish standards. Twenty employees are involved. The operations include cataloging, charging books out, returning books to their proper location, cleaning books, record keeping, packing books for shipment, and handling correspondence. A preliminary investigation resulted in the estimate that 30 percent of the time of the group was spent in cataloging. How many work sampling observations would be made if it were desirable to be 95 percent confident that the observed data were within a tolerance of ±10 percent of the population data? Describe how the random observations should be made.

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Answer:

At least 81 observations should be made to be 95% confident that the observed data is within a tolerance of ±10 percent of the population data.

Step-by-step explanation:

The following equation is used to compute the minimum sample size required to estimate the population proportion  within the required margin of error:

n≥ p×(1-p) × [tex](\frac{z}{ME} )^2[/tex] where

  • n is the sample size
  • p is the estimated proportion of the time of the group was spent in cataloging (30% or 0.30)
  • z is the corresponding z-score for 95% confidence level (1.96)
  • ME is the margin of error (tolerance) in the estimation (10% or 0.10)

Then, n≥ 0.30×0.70 × [tex](\frac{1.96}{0.10} )^2[/tex] ≈ 80.67

At least 81 observations should be made to be 95% confident that the observed data is within a tolerance of ±10 percent of the population data.

Random observations should include different employees, and sampling time should also be random.

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