Question

Supervisor Kenneth Peterson wants to determine the percent of time a machine in his area is idle. He decides to use work sampling, and his initial estimate is that the machine is idle 22% of the time. (Round all intermediate calculations to at least two decimal places before proceeding with further calculations.) The number of observations that need to be taken by Peterson to be 99.00% confident that the results will be less than 5% from the true result=?

Answer 1

To be 99.00% confident that the results will be less than 5% from the true result, Kenneth Peterson would need to take a sample size of approximately 264 observations.

Step-by-step explanation:

To determine the number of observations needed to be 99.00% confident that the results will be less than 5% from the true result, we can use the formula for sample size calculation:

n = (Z * σ / E)^2

Where:

• n is the sample size
• Z is the Z-value corresponding to the confidence level
• σ is the estimated standard deviation
• E is the desired margin of error

In this case, the estimated standard deviation is 22% (0.22) and the desired margin of error is 5% (0.05). The Z-value corresponding to a 99.00% confidence level is 2.58. Plugging these values into the formula, we get:

n = (2.58 * 0.22 / 0.05)^2

n ≈ 263.20

Therefore, Supervisor Kenneth Peterson would need to take a sample size of approximately 264 observations to be 99.00% confident that the results will be less than 5% from the true result.