Exam 8: Statistical Inference: Estimation for Single Populations

If the population is normal and its standard deviation,σ,is known but the sample size is small,z-distribution values may not be used to determine interval estimates for the population mean.

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 estimate the proportion of a population which possesses a given characteristic.A random sample of size 200 is taken and 30% of the sample possesses the characteristic.The 90% confidence interval to estimate the population proportion is ___.

A researcher wants to estimate the proportion of a population which possesses a given characteristic.A random sample of size 250 is taken and 40% of the sample possesses the characteristic.The 95% confidence interval to estimate the population proportion is ___.

In determining the interval estimates for a population variance using the sample variance,it is appropriate to use the values from a chi-square distribution rather than a t distribution.

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

Given n = 17,s² = 18.56,and that the population is normally distributed,the 80% confidence interval for the population variance is ___.

The weights of aluminum castings produced by a process are normally distributed.A random sample of 5 castings is selected;the sample mean weight is 2.21 kilograms;and the sample standard deviation is 0.12 kilograms.The 98% confidence interval for the population mean casting weight 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 ___.

The table t value associated with the upper 10% of the t distribution and 23 degrees of freedom is ___.

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 ___.

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 ___.

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 ___.

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

Suppose a random sample of 36 is selected from a population with a standard deviation of 12.If the sample mean is 98,the 99% confidence interval to estimate the population mean is ___.

Eugene Gates,Marketing Director of Mansfield Motors Manufacturers,Inc.'s Electrical Division,is leading a study to assess the relative importance of product features.An item on a survey questionnaire distributed to 100 of Mansfield's customers asked them to rate the importance of "ease of maintenance" on a scale of 1 to 10 (with 1 meaning "not important" and 10 meaning "highly important").His staff assembled the following statistics: If Eugene concludes that the average rate of "ease of maintenance" for all customers is 7.5,he is using ___.

Elwin Osbourne,CIO at GFS,Inc. ,is studying employee use of GFS email for non-business communications.A random sample of 200 email messages was selected.Thirty of the messages were not business related.The 95% confidence interval for the population proportion is ___.

When the population standard deviation,σ,is unknown the sample standard deviation,s,is used in determining the interval estimate for the population mean.

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 90% confidence interval for the population mean life of the new model is ___.

Estimate the population mean with an unknown population standard deviation using the t statistic and properties of the t distribution.