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HW - Choosing the Sample
Question 1, 13.6.19-T
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It’s believed that as many as of adults over 50 never graduated from high school. We wish to see if this percentage is the same amang the 25 to 30 age group.
a) How mary of this younger age group must we survey in order to estimats the proportion of non-grads to within with confidence?
(Round up to the nearest integer.)

Ask by Cervantes Wright. in the United States
Mar 31,2025

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To estimate the proportion of non-graduates within with confidence, you need to survey 271 individuals from the 25 to 30 age group.

Solución

We use the formula for estimating a proportion within a specified margin of error:
For a confidence level, so that
We are given:
  • An estimated proportion (since are non-grads).
  • A margin of error .
Substitute these values into the formula:
Step 1: Compute :
Step 2: Compute :
Step 3: Compute the numerator:
Step 4: Compute the denominator :
Step 5: Divide the numerator by the denominator:
Since we must round up to the nearest integer, the required sample size is

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Extra Insights

To determine the sample size required for estimating the proportion of non-grads within a specific margin of error and confidence level, the formula to calculate the sample size is given by:
Where is the Z-score corresponding to the desired confidence level (for 90% confidence, ), is the estimated proportion (in this case, 0.20), and is the margin of error (0.04).
So for your situation:
Rounding up, you will need to survey at least individuals in the 25 to 30 age group.
This calculation isn’t just a math exercise; it’s a powerful tool that can help ensure your findings are both precise and trustworthy! Getting the right sample size means you’re on your way to capturing insights about educational attainment accurately!
Have you ever thought about how survey results shape policies? The data you gather can influence education programs targeted at younger adults, highlighting the importance of educational initiatives! So, every participant counts toward enhancing community support systems.

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