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Terrence would like to estimate the mean the number of books students at his school read during the summer. There are 595 students at his school.

Which statements are true?

Select each correct answer.

Responses

The larger the number of students Terrance surveys, the better his estimate of the mean will be.
The larger the number of students Terrance surveys, the better his estimate of the mean will be.

The mean can only be estimated by surveying all 595 students.
The mean can only be estimated by surveying all 595 students.

If Terrance collects a sample of students in the library reading, and surveys them, he can use that data to estimate the mean of the number of books read by all students.
If Terrance collects a sample of students in the library reading, and surveys them, he can use that data to estimate the mean of the number of books read by all students.

To estimate the mean using a sample, Terrance will need to randomly select the students he will survey so that the sample represents the population well.
To estimate the mean using a sample, Terrance will need to randomly select the students he will survey so that the sample represents the population well.

1 answer

Let's evaluate each statement:

  1. The larger the number of students Terrance surveys, the better his estimate of the mean will be.
    True – A larger sample size generally leads to a more accurate estimate of the population mean, as it reduces the margin of error and variability in the estimate.

  2. The mean can only be estimated by surveying all 595 students.
    False – While surveying all students would provide the most accurate mean, it is not necessary. A representative sample can be used to estimate the mean.

  3. If Terrance collects a sample of students in the library reading, and surveys them, he can use that data to estimate the mean of the number of books read by all students.
    False – If the sample is biased (for instance, only including students who read in the library), it may not accurately reflect the entire student population.

  4. To estimate the mean using a sample, Terrance will need to randomly select the students he will survey so that the sample represents the population well.
    True – Random selection helps ensure that the sample is representative of the population, which is critical for making valid inferences about the mean.

Based on this evaluation, the true statements are:

  • The larger the number of students Terrance surveys, the better his estimate of the mean will be.
  • To estimate the mean using a sample, Terrance will need to randomly select the students he will survey so that the sample represents the population well.