AP Statistics : How to find confidence intervals for a difference between two proportions

Study concepts, example questions & explanations for AP Statistics

varsity tutors app store varsity tutors android store

Example Questions

Example Question #2 : Confidence Intervals



Possible Answers:




Correct answer:




Example Question #1 : How To Find Confidence Intervals For A Difference Between Two Proportions

In a simple random sample of  people,  are left-handed. Find a  confidence interval for the true proportion of left-handed people in the entire population.

Possible Answers:

The sample is not sufficiently large. A confidence interval cannot be used.

Correct answer:


Step 1: Determine the approporiate formula. In this case, the statistic is a proportion because the question says 261 people out of 1000 are left-handed. We want to use a confidence interval for proportions. The equation is

Step 2: , or the sample proportion is equal to 

Step 3: The questions asks for a 95% confidence interval. You can assume a normal distribution because of the large sample size. Therefore, in a normal distribution, 95% of the data is contained within .

Step 4: Substitue all the values into the equation to get the answer.

Learning Tools by Varsity Tutors

Incompatible Browser

Please upgrade or download one of the following browsers to use Instant Tutoring: