Probability and Statistics: Confidence Intervals

Construct a 99% confidence interval for the difference between the two proportions in the effectiveness of duct tape versus liquid nitrogen in removing warts.

Calculate the confidence interval for the mean value of normally distributed data using the formula: $\bar{x} \pm z \frac{s}{\sqrt{n}}$, where $\bar{x}$ is the sample mean, $z$ is the z-value for the desired confidence level, $s$ is the standard deviation, and $n$ is the sample size.

Given a dataset where the mean is $\bar{x}$, the sample size is $n$, and the standard deviation is $s$, determine the 95% confidence interval for the mean.

Scores on an exam are normally distributed with a population standard deviation of 5.6. A random sample of 40 scores on the exam has a mean of 32. We want to construct confidence interval estimates for the population mean at 80%, 90%, and 98% confidence levels.

A random sample of 15 observations has a mean of 20 and a standard deviation of 3.5. To estimate the population mean with 95% confidence, determine the margin of error and the confidence interval.

With a sample size of 85, construct a 99% confidence interval for the population mean.

Find the sample size required to estimate the population mean to within 1.5 units where the population standard deviation is 8 at 95% confidence level.

To estimate the population mean to within 1.5 units with 90% confidence, determine the minimum sample size required given the z-critical value is 1.645.

Estimate the average population mean of candy bar lengths from a factory by sampling 100 candy bars and finding a confidence interval for the mean length.

You took a sample of students and found a 95% confidence interval for the true mean amount of sleep to be 7.5 to 8.5 hours. How would you interpret this?

An online poll asked a sample of 850 adult Americans whether they watched any World Cup soccer games. 62% of respondents said they did. What is the Margin of Error for this poll, rounded to the nearest tenth of a percent? What is the 95% confidence interval for the percent of all adult Americans who watched the World Cup?

With 95% confidence, what is the confidence interval for the proportion of voters supporting candidate A?

The average test score of all students in a certain class was measured to be 84 with a standard deviation of 15. If the margin of error was calculated to be 5.367 at a 95% confidence level, how many students were in this class?

Sally wants to determine what proportion of high school students are planning to enroll in college after they graduate. Given a 95% confidence level and a margin of error of 5%, what is the maximum sample size that she should use in order to perform this statistical experiment?

Suppose we wish to estimate the proportion of adults in Ontario that are in favor of harsher penalties for drug offenses. How large of a sample size is required if we wish to estimate $P$ to within $0.03$ with $95\%$ confidence?

Suppose we wish to estimate the proportion of mice that would be killed by a certain dose of a chemotherapy drug. Suppose also that previous studies have shown that approximately $10\%$ of mice are killed by this dose. How large of a sample size is required if we wish to estimate $P$ to within $0.1$ with $99\%$ confidence?