Exam 8: Statistical Inference: Estimation for Single Populations

Velma Vasquez, fund manager of the Vasquez Value Fund, manages a portfolio of 250 common stocks.Velma relies on various statistics, such as variance, to assess the overall risk of stocks in an economic sector.Her staff reported that for a sample 14 utility stocks the mean annualized return was 14% and that the variance was 3%.Assume that annualized returns are normally distributed.The 90% confidence interval for the population variance of annualized returns for utility stocks is _______.

In determining the interval estimates for a population proportion using the sample proportion, it is appropriate to use the z-distribution.

A study is going to be conducted in which the mean of a lifetime of batteries produced by a certain method will be estimated using a 90% confidence interval.The estimate needs to be within +/- 2 hours of the actual population mean.The population standard deviation σ is estimated to be around 25.The necessary sample size should be at least _______.

You are thinking of using a t-table to find a 95 percent confidence interval for the mean μ of a population.The distribution of the population is normal and the population standard deviation is unknown.A random sample of size n is drawn from this population.You may use the t-distribution only if the sample size n is small.

Given the error we are willing to tolerate, the sample size is determined by the mean, µ of the population and the confidence level.

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 100 tellers in the southeast region and determined that their mean training time was 25 hours.Assume that the population standard deviation is 5 hours.The 92% confidence interval for the population mean of training times is ________.

Given n = 20, s = 32, and that the population is normally distributed, the 90% confidence interval for the population variance 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 90% confidence interval for the population mean of waiting times is ________.

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 90% confidence interval to estimate the population proportion is ____.

A researcher wants to estimate the percent of the population that uses the radio to stay informed on local news issues.The researcher wants to estimate the population proportion with a 95% level of confidence.He estimates from previous studies that no more than 30% of the population stay informed on local issues through the radio.The researcher wants the estimate to have an error of no more than .03.The necessary sample size is at least _______.

The employees of Cybertronics Inc.need to complete a certification online.A random sample of 16 employees gives an average time for completion of all the coursework and passing the tests of 20 hours.The population standard deviation is unknown but the sample standard deviation is 6 hours.You can assume that the population of employees is fairly large.Construct a 95% confidence interval for the average time required to complete the certification.

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 point estimate for this population proportion is _______.

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 95% confidence interval for the population variance of waiting times is ________.

The z value associated with a two-sided 90% confidence interval is _______.

A researcher wants to estimate the percent of the population that uses the radio to stay informed on local news issues.The researcher wants to estimate the population proportion with a 90% level of confidence.He estimates from previous studies that no more than 30% of the population stay informed on local issues through the radio.The researcher wants the estimate to have an error of no more than .02.The approximate sample size is at least _______.

Like a t-distribution, a chi-square distribution is symmetrical and extends from minus infinity to plus infinity.

The employees of Cybertronics Inc.need to complete a certification online.A random sample of 49 employees gives an average time for completion of all the coursework and passing the tests of 20 hours.Assume that the population standard deviation is 6 hours and the population of employees is fairly large.Construct a 95% confidence interval for the average time required to complete the certification.

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 95% confidence interval for the population proportion is _________.

A researcher wants to estimate the proportion of the population which possesses a given characteristic.A random sample of size 800 is taken resulting in 360 items which possess the characteristic.The point estimate for this population proportion is _______.

Velma Vasquez, fund manager of the Vasquez Value Fund, manages a portfolio of 250 common stocks.Velma relies on various statistics, such as variance, to assess the overall risk of stocks in an economic sector.Her staff reported that for a sample 14 utility stocks the mean annualized return was 14% and that the variance was 3%.Assume that annualized returns are normally distributed.The 95% confidence interval for the population variance of annualized returns for utility stocks is _______.