Question

A company wants to estimate the mean amount of time (in minutes) that employees commute to work. Find the sample size necessary to estimate the mean with a 2 -min margin of error with 96% confidence. Assume that a previous study showed that the population standard deviation is estimated to be 7.2 min. (7 pts.)

Answer 1

To estimate the mean with a 2-minute margin of error and 96% confidence, a sample size of 55 is necessary.

Step-by-step explanation:

To find the sample size necessary to estimate the mean with a 2-minute margin of error and 96% confidence, we need to use the formula for the sample size for estimating a population mean.

The formula is:

n = (Z * σ / E)^2

where:

• n is the sample size
• Z is the Z-score corresponding to the desired confidence level (in this case, Z = 2.05 for 96% confidence)
• σ is the population standard deviation (given as 7.2 minutes)
• E is the margin of error (given as 2 minutes)

Plugging in the values, we get:

n = (2.05 * 7.2 / 2)^2 = 54.688

Rounding up to the nearest whole number, the sample size necessary is 55.