Exam 8: Statistical Inference: Estimation for Single Populations

The z value associated with a two-sided 80% confidence interval 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 ___.

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

Use the chi-square distribution to estimate the population variance given the sample variance.

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 ___.

A researcher wants to estimate the proportion of the population which possesses a given characteristic.A random sample of size 1800 is taken resulting in 450 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 90% confidence interval for the population variance of annualized returns is ___.

The lengths of steel rods produced by a shearing process are normally distributed.A random sample of 10 rods is selected;the sample mean length is 119.05 centimetres;and the sample standard deviation is 0.10 centimetres.The 95% confidence interval for the population mean rod length is ___.

If the population is normal and its standard deviation,σ,is unknown and the sample size,n,is large (n ≥ 30),interval estimates for the population mean must be determined using z values.

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

James Desreumaux,VP of Human Resources of Maritime Boat Manufacturing (MBM),is reviewing the employee training programs of MBM factories.His staff randomly selected personnel files for 100 workers in New Brunswick and determined that their mean training time was 25 hours.Assume that the population standard deviation is 5 hours.The 95% confidence interval for the population mean of training times is ___.

In estimating the sample size necessary to estimate a population mean,the error of estimation,E,is equal to the difference between the sample mean and the population mean.

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 ___.

Catherine Chao,Director of Marketing Research,is evaluating consumer acceptance of a new toothpaste package.Her staff reports that 17% of a random sample of 200 households prefers the new package to all other package designs.If Catherine concludes that 17% of all households prefer the new package,she is using a ___.

Estimate the population mean with a known population standard deviation with the z statistic,correcting for a finite population if necessary.

Determine the sample size needed in order to estimate the population mean and population proportion.

A researcher conducts a study to determine what the population proportion is for a given characteristic.It is believed from previous studies that the proportion of the population will be at least .65.The researcher wants to use a 98% level of confidence.He also wants the error to be no more than .03.The sample size should be at least ___.

James Desreumaux,VP of Human Resources of Maritime Boat Manufacturing (MBM),is reviewing the employee training programs of MBM factories.His staff randomly selected personnel files for 100 workers in New Brunswick 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 ___.

Catherine Chao,Director of Marketing Research,is evaluating consumer acceptance of a new toothpaste package.She plans to use a 95% confidence interval estimate of the proportion of households which prefer the new packages;she will accept a 0.05 error.Previous studies indicate that new packaging has an approximately 70% acceptance rate.The sample size should be at least ___.

An assumption underlying the use of t statistic in sample-based estimation is that the population is normally distributed.