Unit 7, Lesson 10
Estimating Proportions from Samples
Integrated Math 3
Practice
Problem 1
A scientist captures a sample of fish from 100 different locations along the Yellowstone river and measures the proportion of fish affected by copper toxicity for each sample. Describe how the scientist could use the data to estimate the proportion of fish affected by copper toxicity in the entire population along this portion of the river.
Problem 2
A company produces 1,000 blue crayons every day. A sample of 50 crayons are analyzed, and 3 of them are found to not meet the standards of the company, so they are labeled as defective. A simulation is run in which 50 crayons are chosen out of 1,000 so that each crayon chosen has a 6% chance of being defective. The company runs the simulation 500 times and records each time what proportion of the simulated sample is defective. The standard deviation of that sampling distribution is 0.012.
- What is a good margin of error based on this simulation so that the company can be 95% confident that the interval they construct captures the proportion of all of the crayons that are defective?
- Based on our point estimate and margin of error, is 0.07 a plausible value for the population proportion of crayons that are defective? Explain your reasoning.