Interpreting confidence level example | Confidence intervals | AP Statistics | Khan Academy

TL;DR

A zookeeper used a sample of 30 days to estimate the mean amount of food an elephant eats on a day, resulting in a 90% confidence interval of 341 to 359 kilograms.

Transcript

• [Instructor] We are told that a zookeeper took a random sample of 30 days and observed how much food an elephant ate on each of those days. The sample mean was 350 kilograms, and the sample standard deviation was 25 kilograms. The resulting 90% confidence interval for the mean amount of food was from 341 kilograms to 359 kilograms. Which of the f... Read More

Key Insights

• 😅 The zookeeper is using a sample to estimate the true mean amount of food an elephant eats on a day.
• 👷 A 90% confidence level means that 90% of the constructed confidence intervals will contain the true population mean.
• 🧡 The resulting confidence interval does not determine the range of sample means.
• ❓ The sample mean in the given sample was 350 kilograms, with a 90% confidence interval of 341 to 359 kilograms.
• 👷 This method of constructing confidence intervals provides a reliable estimate of the population mean in about 90% of samples.
• ❓ The sample standard deviation was 25 kilograms.
• ❓ The confidence interval may vary in width depending on the sample.

Questions & Answers

Q: What does a 90% confidence level mean?

A 90% confidence level means that if repeated sampling is done, 90% of the confidence intervals will overlap with the true population mean.

Q: Is the true mean a random variable in this case?

No, the true mean is not a random variable. It represents the actual population mean, and the confidence intervals are constructed to capture it.

Q: Does the confidence interval determine the range of sample means?

No, the confidence interval does not determine the range of sample means. It is solely focused on estimating the true population mean.

Q: How many days were observed in the sample?

The sample consisted of 30 days of observation.

Summary & Key Takeaways

• A zookeeper wants to estimate the mean amount of food an elephant eats on a day.

• They took a sample of 30 days and calculated a sample mean of 350 kilograms.

• The resulting 90% confidence interval is from 341 to 359 kilograms.