Exam 8: Statistical Inference: Estimation for Single Populations

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.

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 ___.

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 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 ___.

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

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

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

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 ___.

A t distribution is similar to a normal distribution, but flatter in the middle.

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 ___.

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.

A random sample of 225 items from a population results in 60% possessing a given characteristic.Using this information, the researcher constructs a 90% confidence interval to estimate the population proportion.The resulting confidence interval 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 ___.

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

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 population proportion with a 90% level of confidence.She estimates from previous studies that the population proportion is no more than .30.The researcher wants the estimate to have an error of no more than .02.The necessary sample size is at least ___.

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 ___.

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 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 ___.

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 ___.