Question
As in Exercise $37,$ we hope to estimate the percentage of adults aged 25 to 30 who never graduated from high school. What sample size would allow us to increase our confidence level to $95 \%$ while reducing the margin of error to only $2 \% ?$
Step 1
The margin of error is given by the formula: $$ E = Z \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} $$ where $E$ is the margin of error, $Z$ is the Z-score, $\hat{p}$ is the estimated proportion, and $n$ is the sample size. Show more…
Show all steps
Your feedback will help us improve your experience
James Kiss and 63 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
As in Exercise 29, we hope to estimate the percentage of adults aged 25 to 30 who never graduated from high school. What sample size would allow us to increase our confidence level to 95% while reducing the margin of error to only 2%?
From the Data at Hand to the World at Large
Confidence Intervals for Proportions
It’s believed that as many as 25% of adults over 50 never graduated from high school. We wish to see if this percentage is the same among the 25 to 30 age group. a) How many of this younger age group must we survey in order to estimate the proportion of non-grads to within 6% with 90% confidence? b) Suppose we want to cut the margin of error to 4%. What’s the necessary sample size? c) What sample size would produce a margin of error of 3%?
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD