Suppose ACT, Inc. wants to update their information from...

Name: Problem 36, Chapter 18: Stats Data and Models
Uploaded: 2022-11-07T23:51:47-08:00
Duration: 1 min 4 s
Channel: James Kiss
Description: Suppose ACT, Inc. wants to update their information from Exercise 34 on the percentage of freshmen that return for a second year of college. a) They want to cut the stated margin of error in half. How many college freshmen must be surveyed? b) Do you have any concerns about this sample? Explain.

Suppose ACT, Inc. wants to update their information from Exercise 34 on the percentage of freshmen that return for a second year of college. a) They want to cut the stated margin of error in half. How many college freshmen must be surveyed? b) Do you have any concerns about this sample? Explain.

Suppose ACT, Inc. wants to update their information from Exercise 34 on the percentage of freshmen that return for a second year of college.
a) They want to cut the stated margin of error in half. How many college freshmen must be surveyed?
b) Do you have any concerns about this sample? Explain.

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Key Concepts

Margin of Error

The margin of error measures the extent of the range that the true population parameter is expected to fall from the sample statistic, given a specific confidence level. In survey research, it is inversely proportional to the square root of the sample size, meaning that to achieve more precise estimates (a smaller margin of error), a larger sample is required.

Sample Size Determination

Determining the required sample size is crucial, as it directly affects the accuracy and reliability of the survey results. In cases where the margin of error is to be reduced by a specific factor (for example, cut in half), the sample size must be increased by the square of that factor, assuming other factors like the confidence level remain constant.

Sampling Bias and Representativeness

Beyond sample size, it is important to consider whether the sample being surveyed is representative of the overall population. Concerns about sampling bias arise if the sample does not accurately reflect the diversity of the population, which can lead to misleading estimates regardless of the precision achieved through a larger sample size.

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