Exam 8: Statistical Inference: Estimation for Single Populations

Brian Vanecek, VP of Operations at Portland Trust Bank, is evaluating the service level provided to walk-in customers.Brian would like to minimize the variance of waiting time for these customers, since this would mean each customer received the same level of service.Accordingly, his staff recorded the waiting times for 15 randomly selected walk-in customers, and determined that their mean waiting time was 15 minutes and that the standard deviation was 4 minutes.Assume that waiting time is normally distributed.The 90% confidence interval for the population variance of waiting times is ________.

A researcher wants to estimate the percent of the population that uses the internet to stay informed on world news issues.The researcher wants to estimate the population proportion with a 98% level of confidence.He estimates from previous studies that at least 65% of the population stay informed on world issues through the internet.He also wants the error to be no more than .03.The approximate sample size should be at least _______.

The table t value associated with the upper 5% of the t distribution and 12 degrees of freedom is _______.

The z value associated with a two-sided 99% confidence interval is _______.

James Desreumaux, VP of Human Resources of American First Banks (AFB), is reviewing the employee training programs of AFB.His staff randomly selected personnel files for 10 tellers in the southwest region, and determined that their mean training time was 25 hours and that the standard deviation was 5 hours.Assume that training times are normally distributed.The 95% confidence interval for the population variance of training times is ________.

A market researcher computed a confidence interval for a population proportion using a 95% confidence level.Her boss decided that she wanted a 99% confidence level instead.The new interval with 99% confidence level will be wider than the original one with a 95% confidence level.

A t-distribution is similar to a normal distribution, but with flatter tails.

The z value associated with a two-sided 88% confidence interval is _______.

Use of the chi-square statistic to estimate the population variance is extremely robust to the assumption that the population is normally distributed.

Suppose a researcher is interested in understanding the variation in the price of store brand milk.A random sample of 36 grocery stores is selected from a population and the mean price of store brand milk is calculated.The sample mean is $3.13 with a standard deviation of $0.23.Construct a 92% confidence interval to estimate the population mean.

A large national company is considering negotiating cellular phone rates for its employees.The Human Resource department would like to estimate the proportion of its employee population who own an Apple iPhone.A random sample of size 250 is taken and 40% of the sample own and iPhone.The 95% confidence interval to estimate the population proportion is _______.

A random sample of 64 items is selected from a population of 400 items.The sample mean is 200.The population standard deviation is 48.From these data, the 95% confidence interval to estimate the population mean would be _______.

Given n = 12, s² = 44.90, and that the population is normally distributed, the 99% confidence interval for the population variance is ________.

A researcher wants to determine the sample size necessary to adequately conduct a study to estimate the population mean to within 5 points.The range of population values is 80 and the researcher plans to use a 90% level of confidence.The sample size should be at least _______.

Catherine Chao, Director of Marketing Research, is evaluating consumer acceptance of a new toothpaste package.She randomly selects a sample of 200 households.Forty households prefer the new package to all other package designs.The point estimate for this population proportion is _______.

Elwin Osbourne, CIO at GFS, Inc., is studying employee use of GFS e-mail for non-business communications.A random sample of 200 e-mail messages was selected.Thirty of the messages were not business related.The 98% confidence interval for the population proportion is _________.

Brian Vanecek, VP of Operations at Portland Trust Bank, is evaluating the service level provided to walk-in customers.Accordingly, his staff recorded the waiting times for 64 randomly selected walk-in customers and determined that their mean waiting time was 15 minutes.Assume that the population standard deviation is 4 minutes.The 95% confidence interval for the population mean of waiting times is ________.

Suppose a researcher is interested in understanding the variation in the price of store brand milk.A random sample of 36 grocery stores is selected from a population and the mean price of store brand milk is calculated.The sample mean is $3.13 with a standard deviation of $0.23.Construct a 99% confidence interval to estimate the population mean.

Suppose the fat content of a hotdog follows normal distribution.Ten random measurements give a mean of 21.77 and standard deviation of 3.69.The 90% confidence interval for the population variance of fat content of a hotdog is ________

An insurance company is interested in conducting a study to estimate the population proportion of teenagers who obtain a driving permit within 1 year of their 16^th birthday.A level of confidence of 99% will be used and an error of no more than .04 is desired.There is no knowledge as to what the population proportion will be.The approximate sample size should be at least _______.