Exam 8: Statistical Inference: Estimation for Single Populations

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

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

A large trucking company wants to estimate the proportion of its tracker truck population with refrigerated carrier capacity..A random sample of 200 tracker trucks is taken and 30% of the sample have refrigerated carrier capacity.The 95% confidence interval to estimate the 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 90% confidence interval for the population variance of waiting times 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 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 this data,a 90% confidence interval to estimate the population mean can be computed as _______.

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 _______.

In order to find values in the t distribution table,you must determine the appropriate degrees of freedom based on the sample sizes.

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 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 necessary sample size is at least _______.

James Desreumaux,VP of Human Resources of American First Banks (AFB),is reviewing the employee training programs of AFB banks.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 88% confidence interval for the population mean of training times is ________.

A random sample of 225 items from a population results in 60% possessing a given characteristic.Using this information,the researcher constructs a 99% confidence interval to estimate the population proportion.The resulting confidence interval is _______.

An insurance company is interested in conducting a study to 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 size of sample should be at least _______.

Suppose a random sample of 16 is selected from a population with a normal distribution with a known population standard deviation σ of 10.Assume that the sample mean is 4.2.Based on a 90% confidence interval for the population mean,we can conclude that 0.1 is a plausible number for the population mean μ.

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.

Life tests performed on a sample of 13 batteries of a new model indicated: (1)an average life of 75 months,and (2)a standard deviation of 5 months.Other battery models,produced by similar processes,have normally distributed life spans.The 98% confidence interval for the population mean life of the new model is _________.

If the standard deviation, is known the z-distribution values may not be used to determine interval estimates for the population mean when

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 90% confidence interval for the population proportion is _________.

Elwin Osbourne,CIO at GFS,Inc.,is studying employee use of GFS e-mail for non-business communications.He plans to use a 95% confidence interval estimate of the proportion of e-mail messages that are non-business; he will accept a 0.05 error.Previous studies indicate that approximately 30% of employee e-mail is not business related.Elwin should sample _______ e-mail messages.