University:
University of California, San Diego
Course:
CSE 100/101 | Data Structures and Algorithms
Academic year:

2023
Views:

481

Pages:

3
Author:

Sol Kwon

Stat 2 Lab #18: Estimation and confidence intervals for the population percentage Learning objectives: • Calculate the expected values and SEs for a sample percentage • Compute confidence intervals for the population percentage • Use CLT and rules of thumb to determine if computing a confidence interval using the normal table is appropriate 1. A simple random sample of 3,500 people age 18 or over is taken in a large town to estimate the percentage of people (age 18 or over in the town) who read newspapers. It turns out that 2,487 people in the sample are newspaper readers. (a) Make a 0-1 box by “plugging in” the fraction of 1’s and 0’s from the sample. (Note: I have not given you the population size, but that’s ok, as long as the fraction of 1’s and 0’s match what you see in the sample.) (b) What is the estimated population percentage and the associated standard error? (c) If it is appropriate, find a 95%-confidence interval for the percentage of all newspaper readers in the town (age 18 or over). If it is not appropriate, explain why not. 2. A survey organization takes a simple random sample of 1,500 people from the residents of a large city, with population 800,000. Among the sampled people, 1,035 were renters. (a) Fill in the blanks below with either “exactly equal to” or “estimated from the data to be”: The expected value for the percentage of sampled people who rent is ________________________________________ 69%. The SE for the percentage of sampled people who rent is ________________________________________ 1.2%. (b) Now check the math from part (a). Are 69% and 1.2% correct? (c) Fill in the blank: A 90% confidence interval for __________________________________________________________________ goes from about 67% to about 71%. (d) Check the math from part (c). 3. A political organization with 100,000 members takes a simple random sample of 1,000 members and asks for their annual income in 2018. The sample average is $25,000, with a standard deviation of $20,000. 30% of the sampled members reported incomes over $50,000. A box model will be used to estimate the percentage of all the members in the organization with incomes over $50,000. (a) The tickets in the box have values of (circle one): 0 or 1 OR incomes in dollars (b) TRUE or FALSE (circle one): The histogram of the incomes in the sample approximately follows the normal curve. Explain your answer. (c) TRUE or FALSE (circle one): The probability histogram of sample percentage of members with incomes over $50,000 approximately follows the normal curve. Explain your answer. (d) Calculate a 95%-confidence interval for the percentage of all members with incomes over $50,000.