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You have 24 students in your school that you survey about mental health during the COVID pandemic while still trying to manage being a student. Out of the 24 students surveyed, 8 reported feeling depressed, and 18 reported feeling stressed. You also had them take the GAD-7 to measure the level of anxiety, which had the following scores:

[tex]\[ 1, 2, 2, 4, 5, 6, 8, 9, 10, 10, 10, 11, 12, 13, 13, 14, 14, 14, 14, 14, 17, 18, 20, 21 \][/tex]

A score of 10 or higher indicates anxiety. Answer the following questions. Be sure to write out the entire formula, answer, and all the steps.

Would you use [tex]\( n \)[/tex] or [tex]\( N \)[/tex]? Once you decide, write out what your [tex]\( n \)[/tex] or [tex]\( N \)[/tex] is in a proper formula.

- [tex]\( n = 18 \)[/tex]
- [tex]\( n = 24 \)[/tex]
- [tex]\( N = 24 \)[/tex]
- [tex]\( N = 18 \)[/tex]

Answer :

To solve the problem of determining whether to use 'n' or 'N', and what value it should hold, you need to understand the context in which these symbols are typically used in statistics.

1. Understanding 'n' and 'N':
- 'n' usually represents the sample size. This is the number of observations or individuals that are part of a study or survey.
- 'N' typically represents the population size, meaning the total number of individuals in the entire group that could possibly be studied.

2. Identify the context:
- In the given scenario, a survey was conducted with a specific set of students. This indicates you are working with a sample, not the entire population of a larger group.
- The survey is specific to the students you have data for, not all possible students everywhere.

3. Determining the correct symbol and value:
- Since the survey was specifically conducted with 24 students, this group of 24 is your sample from a potentially larger population of all students.
- Therefore, you would use 'n' to represent the sample size in this context.

4. Conclusion:
- 'n' is used when specifically referring to the number of subjects in your sample.
- In this case, 'n' represents the number of students surveyed, which is 24.

So, the correct symbol and value to use for this scenario is [tex]\( n = 24 \)[/tex]. This indicates that the sample size for your survey is 24 students.

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Rewritten by : Barada