8. Sampling Distributions & Confidence Intervals: Proportion

A factory manager wants to estimate the proportion of defective items produced. In a batch of 20 items, the factory has produced 6 with defects. Find the margin of error for a 98% confidence interval for the true proportion of defective items.

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. 

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? 

A labor economist wants to estimate, with $90\%$ confidence, the proportion of remote workers in the workforce. The economist wants the estimate to be accurate within $4\%$ of the true population proportion. What is the minimum sample size needed for this estimate?