Exam 10: Confidence Intervals

The manager of City Pizza wanted to estimate the mean amount spent per customer at his shop on Friday nights. From a sample of 50 Friday night receipts, he determined that the mean amount spent per customer was $15.50. Assume that the amount spent per customer on Friday nights is normally distributed with a standard deviation of $2.00. Construct a 98% confidence interval for the true mean amount each customer spent on Friday nights.

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 these proportions, which one would produce the narrowest 95% confidence interval for the population proportion?

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 ___.

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

Catherine Chao, Director of Marketing Research, is evaluating consumer acceptance of a new toothpaste package. Her staff reports that 17% of a random sample of 200 households prefers the new package to all other package designs. If Catherine concludes that 17% of all households prefer the new package, she is using ___.

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 t score (or table value for Student's t distribution) associated with the upper 5% and 48 degrees of freedom is ___.

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

A study is going to be conducted in which a mean of a lifetime of batteries produced by a certain method will be estimated using a 90% confidence interval. The estimate needs to be within +/- 2 hours of the actual population mean. The population standard deviation σ is estimated to be around 25. The necessary sample size should be at least ___.

If the population is normal and its standard deviation σ is known, and the sample size n is large (n ≥ 30), interval estimates for the population mean must be determined using z values.

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 ___.

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 5% of the t distribution and 12 degrees of freedom is ___.

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 95% confidence interval to estimate the population proportion is ___.

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 $\textbf{ not }$ business related. The 98% confidence interval for the population proportion 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 point estimate for the proportion of the population that uses this method 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 ___.

If you need to estimate the population mean within 2.5 units and with a confidence level of 95%, the minimum value observed is 15 and the maximum 65. What sample size would you use?

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