Answer:
To determine the minimum sample size needed to estimate the mean
with a desired margin of error, we can use the formula for sample size
calculation:
n = (2) 2
Where:
- n = sample size
- Z = Z-score corresponding to the desired level of confidence (e.g., for a 95% confidence level, Z = 1.96) - r = standard deviation of the population (miles per month in this case)
- E = margin of error (desired precision of the estimate)
Given that the standard deviation is in miles per month and we want the estimate to be within E miles per month, we can plug in these values to calculate the minimum sample size needed.
For example, if we want the estimate to be within 10 miles per month with a 95% confidence level, we can use the formula with Z=1.96 (for 95% confidence) and the given standard deviation:
n = (1.96.0)
This will give us the minimum sample size required to ensure that the estimate is within 10 miles per month with 95% confidence.
By calculating the sample size using the formula above, the consumer group can be confident that their estimate of the mean rental car mileage is within the desired margin of error.
Remember to adjust the values in the formula based on the specific confidence level and margin of error required for the estimation.