5. Statistical Inference

Confidence Intervals — Quiz

Test your understanding of confidence intervals with 5 practice questions.

Practice Questions

Question 1

A sample of 49 observations is drawn from a population. The sample mean is 100, and the sample standard deviation is 14. Assuming a 95% confidence level and using the $t$-distribution, what is the margin of error? (Use $t = 2.021$ for 95% confidence with 48 degrees of freedom.)

Question 2

A researcher wants to estimate the average weight of a certain species of fish. A sample of 64 fish is taken, and the sample mean weight is 5 kg. The population standard deviation is known to be 1.2 kg. What is the 95% confidence interval for the population mean weight? (Use $z = 1.96$ for 95% confidence.)

Question 3

A random sample of 81 observations is drawn from a population. The sample mean is 75, and the population standard deviation is 9. What is the 90% confidence interval for the population mean? (Use $z = 1.645$ for 90% confidence.)

Question 4

A sample of 100 people is taken to estimate the proportion of voters who support a certain candidate. The sample proportion is 0.55. What is the 95% confidence interval for the population proportion? (Use $z = 1.96$ for 95% confidence.)

Question 5

A researcher takes a sample of 36 observations from a population. The sample mean is 90, and the population standard deviation is 18. What is the 98% confidence interval for the population mean? (Use $z = 2.326$ for 98% confidence.)