Question

Suppose the average commute time of your employees is unknown. The standard deviation of their commute time is estimated as 32.5 minutes. How many employees must be included in a sample to create a 95 percent confidence interval for the average commute time with a confidence interval width of no more than 15 minutes?

Answer 1

To create a 95 percent confidence interval for the average commute time with a confidence interval width of no more than 15 minutes, you need a sample size of 35 employees.

Step-by-step explanation:

To create a 95 percent confidence interval for the average commute time with a confidence interval width of no more than 15 minutes, we need to determine the required sample size. The formula for the sample size in this case is:

n = (Z * σ / E)²

Where:

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• n is the required sample size
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• Z is the Z-score for the desired confidence level (95% corresponds to a Z-score of 1.96)
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• σ is the estimated standard deviation (32.5 minutes in this case)
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• E is the desired margin of error (15 minutes in this case)

Plugging in the values, we can calculate the required sample size as:

n = (1.96 * 32.5 / 15)² = 34.86

Since we cannot have a fractional number of employees, we need to round up to the nearest whole number. Therefore, we need a sample size of 35 employees to create a 95 percent confidence interval for the average commute time with a confidence interval width of no more than 15 minutes.