Exam 8: Statistical Inference: Estimation for Single Populations

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. Ea5e of Maintenance Mean 7.5 Standard Deviation 1.5 If Eugene concludes that the average rate of "ease of maintenance" for all customers is 7.5, he is using ________.

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.

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 95% confidence interval for the population mean of training times 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 _________.

A researcher wants to estimate the proportion of manufacturing companies that use the six sigma method.For this purpose, she takes a random sample of 50 manufacturing companies and finds out that 28 of them employ this method.The 95% confidence interval for the proportion of manufacturing companies that use six sigma is ______.

If the population is not normal but its standard deviation, σ is known and the sample size, n is large (n ≥ 30), z-distribution values may be used to determine interval estimates for the population mean.

You need to determine the population variance of the diameters of a specialized electronic component used for a new product.Other studies indicate that the diameters of this product are roughly normally distributed.You take a sample of 15 units and find out that the sample average diameter is 0.24 mm, and the sample standard deviation is 0.2 mm.What is the 95% confidence interval for the population variance?

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 _______.

A researcher wants to estimate the proportion of the manufacturing companies that use the six sigma method.For this purpose, she will take a random sample of 50 manufacturing companies and find out how many of them use this method.She estimates that the proportion will be anywhere from 0.4 to 0.55.Of all the proportions in that range, which one would produce the narrowest 95% confidence interval for the population proportion?

A researcher is interested in estimating the mean weight of a semi tractor truck to determine the potential load capacity.She takes a random sample of 17 trucks and computes a sample mean of 20,000 pounds with sample standard deviation of 1,500.She decides to construct a 98% confidence interval to estimate the mean.The degrees of freedom associated with this problem are _______.

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 88% confidence interval for the population mean of training times is ________.

In estimating the sample size necessary to estimate p, if there is no good approximation for the value of p available, the value of ____ should be used as an estimate of p in the formula.

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 _________.

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 _________.

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 90% confidence interval for the population proportion is _________.

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 _______.

The z-distribution is used to estimate a population mean for large samples if the population standard deviation is known."Large" is usually defined as _______.

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 closest to ______.

A researcher wants to estimate the proportion of manufacturing companies that use the six sigma method.For this purpose, she takes a random sample of 50 manufacturing companies and finds out that 28 of them employ this method.The point estimate for the proportion of the population that uses this method is ______.