Answer:
We need to consider a few things, such as
- How much margin of error does the principal want? (Margin of error is the range of values around our average estimate, where we can be confident that the actual population mean lies. The smaller the margin of error, the more accurate our estimate will be).
- How much variability is there in the time it takes buses to arrive and drop off students? (If there is high variability, we need a larger sample to get an accurate estimate).
- How many resources are available to collect data? (If resources are limited, we may need to use a smaller sample).
Given these factors, I would recommend a sample of at least 30 buses. This sample should be randomly selected from all buses that transport students to Riverside High School.
Here are the steps that the principal can take to estimate the average time it takes each bus to arrive and drop off students each day :
- Randomly select a sample of at least 30 buses.
- Record the time it takes each bus to arrive and drop off students on a particular day.
- Calculate the average time it takes all buses in the sample to arrive and drop off students.
- Use the sample mean to estimate the population mean.
Step-by-step explanation:
The first step is to determine the margin of error that the principal is willing to accept. This will determine how large a sample is needed to get an accurate estimate. A smaller margin of error will require a larger sample.
The second step is to assess the variability in the time it takes buses to arrive and drop off students. If there is a lot of variability, then a larger sample will be needed to get an accurate estimate.
The third step is to consider the resources available for collecting data. If resources are limited, then a smaller sample may be necessary.
Based on these factors, I recommend a sample of at least 30 buses. This will provide a good balance between accuracy and resources.
The steps outlined in the second half of the text are the standard steps for estimating a population mean from a sample.