Question

The population standard deviation for time spent in an entry level position is 542 days. if we want to be 90% confident that the sample mean is within 141 days of the true population mean, use a calculator to find the minimum sample size that should be taken. be sure to round up to the nearest integer.

Answer 1

To achieve a 90% confidence level with a margin of error of 141 days given a population standard deviation of 542 days, the minimum sample size required is 312, rounded up from 311.102.

Step-by-step explanation:

To find the minimum sample size (n) needed for a 90% confidence level with a margin of error (E) of 141 days and a known population standard deviation (σ) of 542 days, we can use the formula for the sample size of a mean:

n = (Z²σ²) / E²

Where Z is the Z-score corresponding to the 90% confidence level. Utilizing a Z-score table or calculator, we find that the Z-score for a 90% confidence level is approximately 1.645. Now we can plug in the values:

n = (1.645² × 542²) / 141²

This yields:

n = (2.706² × 293,764) / 19,881

n ≈ 21.051 × 14.781

n ≈ 311.102

Since we can't have a fraction of a person, we'll round up to the nearest whole number:

Minimum sample size = 312

Therefore, a minimum of 312 participants should be sampled to achieve the desired confidence level and precision.