Exam 9: Confidence Intervals

Recently, a case of food poisoning was traced to a particular restaurant chain. The source was identified, and corrective actions were taken to make sure that the food poisoning would not reoccur. Despite the response from the restaurant chain, many consumers refused to visit the restaurant for some time after the event. A survey was conducted three months after the food poisoning occurred, with a sample of 319 former customers contacted. Of the 319 contacted, 29 indicated that they would not go back to the restaurant because of the potential for food poisoning. What sample size would be needed in order to be 99 percent confident that the sample proportion is within .02 of ρ, the true proportion of customers who refuse to go back to the restaurant?

In a random sample of 651 computer scientists who subscribed to a web-based daily news update, it was found that the average salary was $46,816 with a population standard deviation of $12,557. Calculate a 91 percent confidence interval for the mean salary of computer scientists.

The more variable that the population measurements are, the larger the sample size that is needed to accurately estimate µ at a specific confidence level.

Assuming the same level of significance α, as the sample size increases, the value of t_α/2 approaches the value of z_α/2.

The width of a confidence interval will be

A company is interested in estimating μ, the mean number of days of sick leave taken by its employees. Their statistician randomly selects 100 personnel files and notes the number of sick days taken by each employee. The sample mean is 12.2 days, and the sample standard deviation is 10 days. How many personnel files would the statistician have to select in order to estimate μ to within 2 days with a 99 percent confidence interval?

The internal auditing staff of a local lawn-service company performs a sample audit each quarter to estimate the proportion of accounts that are current (between 0 and 60 days after billing). The historical records show that over the past 8 years 70 percent of the accounts have been current. Determine the sample size needed in order to be 99 percent confident that the sample proportion of the current customer accounts is within .03 of the true proportion of all current accounts for this company.

The internal auditing staff of a local lawn-service company performs a sample audit each quarter to estimate the proportion of accounts that are delinquent (more than 90 days overdue). For this quarter, the auditing staff randomly selected 400 customer accounts and found that 80 of these accounts were delinquent. What is the 95 percent confidence interval for the proportion of all delinquent customer accounts at this company?

A sociologist develops a test designed to measure attitudes about disabled people and gives the test to 16 randomly selected subjects. Their mean score is 71.2 with a standard deviation of 10.5. Construct the 99 percent confidence interval for the mean score of all subjects.