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.

1. 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?
2. 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.

A researcher uses a random sample of 200 people in prison in the United States to find that the proportion of the prison population that is jailed for drug-related crimes is 0.485. The researcher simulates selecting a sample of 200 people in prison, each with a 48.5% chance of being in prison for drug-related crimes. The simulation is run 400 times, and the results are shown in the histogram. Use the histogram and information from the original sample to estimate the proportion of people in the United States that are in prison for drug-related crimes. Be sure to include a margin of error with your estimate.

Histogram from point 4 to point 5,8 by point 0,2’s. Proportion of prisoners convicted of drug related crimes. Beginning at 0 point 4 up to but not including 0 point 5,8, height of each bar is 7, 28, 45, 81, 92, 89, 31, 19, 8.

An advertising company is interested in the average number of ads clicked on each year by people at a certain website. They randomly select 25 visitors and determine the number of ads they clicked on in the previous year. After looking at the sample mean, the company runs simulations of repeatedly sampling 25 visitors, and estimates that the mean number of ads clicked on is 6.4 with a margin of error of 1.3 ads. Based on these values, what interval is likely to contain the true mean number of ads clicked on in the previous year by the population?

Based on surveys of a random sample from students at a university and a model of the sampling distribution, the proportion of university students interested in a new chain restaurant opening on their campus is 0.62, and the standard deviation of the sampling distribution model is 0.04. Which of these is the smallest interval that we can be 95% confident will contain the proportion of all students at the university interested in the new restaurant?

Kiran collects information about 25 classmates. He believes his data set is perfectly symmetrical with a mean and median of 6. He then realizes that the number he has recorded as 12 is actually supposed to be 10. What is true about the mean and median of his corrected data set?