8. Sampling Distributions & Confidence Intervals: Proportion

Your company has asked you to estimate the proportion of people who prefer the color red over other primary colors for manufacturing purposes. If they want the estimate to be within $.01$ of the true proportion with $95\%$ confidence, how many people should you survey?  

You want to make a $97\%$ confidence interval for the population proportion of people between $20-30$ years old who have gotten a speeding ticket in the past $2$ years. A prior study found that $26\%$ of people between $20-30$ years old have received a speeding ticket in the last year. If you want your estimate to be accurate within $3\%$ of the true population proportion, what is the minimum sample size needed? 

Which type of variable is required to construct a confidence interval for a $p$ (population proportion)?

A health clinic is studying the effectiveness of a new flu vaccine. In a random sample of 80 patients who received the vaccine, 68 did not get the flu during the season. Make a 99% confidence interval for the true proportion of vaccinated individuals who are protected from the flu.

We are ___% confident that between (_––––,_––––) of vaccinated individuals are protected from the flu. 

You wish to estimate with $90\%$ confidence the population proportion of people in Gen-Z that use social media. If you want your estimate to be accurate within $4\%$ of the population proportion, what is the minimum sample size needed? 

A previous study found that your school consists of $60\%$ White/Caucasian students. You want the $98\%$ confidence interval for the proportion of White/Caucasian students to be no more than $.05$ away from the true proportion. How many students must you include in a sample to create this confidence interval? 

Make a confidence interval for $p$ given the following values.

$x=314,n=500,C=99\%$

Over the first $20$ days of the semester, one student is late to class on $6$ days. Construct a $98\%$ confidence interval for the true proportion of time this student is late. 

Make a confidence interval for $p$ given the following values.

$\hat{p}=0.15,n=60,C=90\%$

Over the first $20$ days of the semester, one student is late to class on $6$ days. Find the margin of error for a $98\%$ confidence interval for the true proportion of time this student is late.