Exam 10: Confidence Intervals

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 employees of Cybertronics Inc. need to complete a certification online. A random sample of 49 employees gives an average time for completion of all the coursework and passing the tests of 6 hours. Assume that the population standard deviation is 6 hours and the population of employees is fairly large. Construct a 95% confidence interval for the average time required to complete the certification.

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 an iPhone. The 90% confidence interval to estimate the population proportion is ___.

A researcher wants to estimate the percent of the population that uses the radio to stay informed on local news issues. The researcher wants to estimate the population proportion with a 95% level of confidence. He estimates from previous studies that no more than 30% of the population stay informed on local issues through the radio. The researcher wants the estimate to have an error of no more than.03. The necessary sample size is at least ___.

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

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

James Desreumaux, VP of Human Resources of American First Banks (AFB), is reviewing the employee training programs of AFB banks. 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 92% confidence interval for the population mean of training times 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 90% confidence interval for the population mean of waiting times is ___.

A random sample of 64 items is selected from a population of 400 items. The sample mean is 200. The population standard deviation is 48. From this data, a 95% confidence interval to estimate the population mean can be computed as ___.

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 researcher is interested in estimating the mean weight of a semi-tracker 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. The 90% confidence interval for the population mean rod length is ___.

A researcher is interested in estimating the mean weight of a semi-tracker 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 ___.

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

The z value associated with a two-sided 95% confidence interval 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 ___.

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

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 ___.

A t distribution is similar to a normal distribution, but with flatter tails.

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 ___.

An insurance company is interested in conducting a study to estimate the population proportion of teenagers who obtain a driving permit within 1 year of their 16^th birthday. A level of confidence of 99% will be used and an error of no more than.04 is desired. There is no knowledge as to what the population proportion will be. The size of sample should be at least ___.