Exam 8: Statistical Inference: Estimation for Single Populations

For a new product,you need to determine the average diameter of a specialized electronic component,which will be a critical component of the new product.You measure the diameter in a sample of size 15 and find an average diameter of 0.24 mm,with a standard deviation of 0.02 mm.Other studies indicate that the diameter of similar products is normally distributed.The 99% confidence interval for the average diameter of this electronic component 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 _______.

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

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

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.

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 45 randomly selected walk-in customers,and calculated that their mean waiting time was 15 minutes.If Brian concludes that the average waiting time for all walk-in customers is 15 minutes,he is using a ________.

A study is going to be conducted in which a population mean will be estimated using a 92% confidence interval.The estimate needs to be within 12 of the actual population mean.The population variance is estimated to be around 2500.The necessary sample size should be at least _______.

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 _______.

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 pounds; and the sample standard deviation is 0.12 pound. The 98% confidence interval for the population mean casting weight is _________.

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 ________

When a range of values is used to estimate a population parameter,it is called a range estimate.

Suppose a researcher is interested in understanding the variation in the price of store brand milk.A random sample of 36 grocery stores 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.

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 _______.

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 _________.

The z value associated with a two?sided 88% 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 _______.

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

When a statistic calculated from sample data is used to estimate a population parameter,it is called a point estimate.

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 _______.