Exam 9: Estimation and Confidence Intervals

A student wanted to construct a 95% confidence interval for the mean age of students in her statistics class. She randomly selected nine students. Their mean age was 19.1 years, with a sample standard deviation of 1.5 years. What is the 95% confidence interval for the population mean?

A silkscreen printing company purchases t-shirts. To ensure the quality of the shipment, 300 t-shirts are randomly selected. Fifteen are defective. What is the 95% confidence interval for the proportion defective?

A survey of 16 executives showed a mean work time per week of 50 hours, with a standard deviation of 10 hours. What is the 95% confidence interval for the population mean?

A survey of an urban university (population of 25,450) showed that 750 of 1,100 students sampled attended a home football game during the season. Using the 90% level of confidence, what is the confidence interval for the proportion of students attending a football game?

Mileage tests were conducted on a randomly selected sample of 100 newly developed automobile tires. The results showed that the mean tread life was 50,000 miles, with a standard deviation of 3,500 miles. What is the best estimate of the mean tread life in miles for the entire population of these tires?

When estimating a population mean with a confidence interval, a smaller margin of error requires a _________ sample size.

When the population standard deviation is unknown, a __________ statistic is used to compute a confidence interval.

A group of statistics students decided to conduct a survey at their university to find the average (mean) amount of time students spent studying per week. They sampled 240 students and found a mean of 22.3 hours per week. Assuming a population standard deviation of six hours, what is the 99% level of confidence?

A local grocery store wants to estimate the mean daily number of gallons of milk sold to customers. Assume the number of gallons sold follows the normal distribution, with a population standard deviation of 5.10 gallons. A random sample of 60 days shows that the mean daily number of gallons sold is 10.00. Compute a 99% confidence interval for the population mean.

A university surveyed recent graduates of the English Department for their starting salaries. Four hundred graduates returned the survey. The average salary was $25,000, with a standard deviation of $2,500. What is the best point estimate of the population mean?

A research firm needs to estimate within 3% the proportion of junior executives leaving large manufacturing companies within three years. A 0.95 degree of confidence is to be used. Several years ago, a study revealed that 21% of junior executives left their company within three years. To update this study, how many junior executives should be surveyed?

A survey of 50 retail stores revealed that the average price of a microwave was $375, with a sample standard deviation of $20. Assuming the population is normally distributed, what is the 95% confidence interval to estimate the true cost of the microwave?

A confidence interval for a population mean __________.

A local politician wants an estimate of the proportion of the population who support her fiscal policies. She wants the estimate to be within .06 of the true proportion. Assume a 95% level of confidence. The politician's advisors estimated the proportion supporting her fiscal policy to be .60. How large of a sample is required?

A group of statistics students decided to conduct a survey at their university to find the average (mean) amount of time students spent studying per week. Assuming a population standard deviation of six hours, what is the required sample size if the error should be less than a half hour with a 95% level of confidence?

An interval estimate is a single value used to estimate a population parameter.

A survey of 25 grocery stores revealed that the mean price of a gallon of milk was $2.98, with a standard error of $0.10. If 90% and 95% confidence intervals were developed to estimate the true cost of a gallon of milk, what similarities would they have?

How is the t distribution similar to the standard z distribution?

There are 2,000 eligible voters in a precinct. A total of 500 voters are randomly selected and asked whether they plan to vote for the Democratic incumbent or the Republican challenger. Of the 500 surveyed, 350 said they would vote for the Democratic incumbent. Using the 0.99 confidence coefficient, what are the confidence limits for the proportion that plan to vote for the Democratic incumbent?

A z statistic is used for a problem involving any sample size and an unknown population standard deviation.