Exam 9: Confidence Intervals

In 2005, 13,000 Internet users were surveyed and asked about their willingness to pay fees for access to websites. Of these, 2,938 were definitely not willing to pay such fees. Construct a 95 percent confidence interval for the proportion definitely unwilling to pay fees.

As the significance level α increases, the width of the confidence interval ________.

When establishing the confidence interval for the average weight of a cereal box, assume that the population standard deviation is known to be 2 ounces and is normally distributed. Based on a sample, the average weight of a sample of 20 boxes is 16 ounces. The appropriate test statistic to use is ________.

When sample size is 20, find t_.10.

A federal bank examiner is interested in estimating the mean outstanding defaulted loans balance of all defaulted loans over the last three years. A random sample of 20 defaulted loans yielded a mean of $67,918 with a standard deviation of $16,552.40. Calculate a 90 percent confidence interval for the mean balance of defaulted loans over the past three years.

What sample size is needed to obtain a 95 percent confidence interval for the proportion of fat in meat that is within 3 percent of the true value?

When the level of confidence and sample proportion remain the same, a confidence interval for a population proportion p based on a sample of n = 100 will be ________ a confidence interval for p based on a sample of n = 400.

The coffee and soup machine at the local subway station is supposed to fill cups with 6 ounces of soup. Ten cups of soup are bought with results of a mean of 5.93 ounces and a standard deviation of .13 ounces. Construct a 99 percent confidence interval for the true machine-fill amount.

If σ is unknown and there is no preliminary sample available to estimate σ, the range divided by four can be utilized to determine an estimate of σ when finding sample size.

An insurance company estimates 45 percent of its claims have errors. The insurance company wants to estimate with 99 percent confidence the proportion of claims with errors. What sample size is needed if they wish to be within 5 percent of the actual?

A sample of 2,000 people yielded = .52. What is the variance of the population proportion?

A company is interested in estimating μ, the mean number of days of sick leave taken by its employees. Their statistician randomly selects 100 personnel files and notes the number of sick days taken by each employee. The sample mean is 12.2 days, and the sample standard deviation is 10 days. Calculate a 95 percent confidence interval for μ.

The state highway department is studying traffic patterns on one of the busiest highways in the state. As part of the study, the department needs to estimate the average number of vehicles that pass an intersection each day. A random sample of 64 days gives us a sample mean of 14,205 cars and a sample standard deviation of 1,010 cars. What is the 98 percent confidence interval estimate of μ, the mean number of cars passing the intersection?

A sample of 2,000 people yielded =.52. Calculate a 99 percent confidence interval for p.

You want to estimate the proportion of customers who are satisfied with their experiences at a local supermarket at α = .10 and within .025 of the true value. It has been estimated that p =.85. How large of a sample is needed?

The state agriculture department tested 203 fuel samples across the state in 2009 for accuracy of the reported octane level. For premium grade, 14 out of 105 samples failed. Find a 99 percent confidence interval for the true population proportion of premium grade fuel-quality failures.

The t distribution always has n degrees of freedom.

A statistical quality control process for cereal production measures the weight of a cereal box. The population standard deviation is known to be .06 ounces. In order to achieve 97 percent confidence with a margin of error of .02 ounces, how large a sample should be used?

Assuming the same level of significance α, as the sample size increases, the value of t_α/2 ________ approaches the value of z_α/2.

When constructing a confidence interval for a population mean, if a population is normally distributed and a small sample is taken, then the distribution of is based on ________.