Exam 6: Confidence Intervals and Sample Size

The width of a confidence interval for a population mean that is based on the t-distribution varies from sample to sample even if the sample size and confidence level is kept fixed.

The symbol for the sample proportion is __________. ________________________________________

A report states that 40% of home owners had a vegetable garden. How large a sample is needed to estimate the

Find the 95% confidence interval for the variance of the lengths of pipes if a sample of 16 pipes has a standard deviation of 12 inches.

A quality control expert wants to estimate the proportion of defective components that are being manufactured by his company to within 2.5%. A sample of 300 components showed that 20 were defective. How large a sample is needed to estimate the

\text { Find the value of \& #61537; as shown in the figure below. }

A survey of 800 women shoppers found that 17% of them shop on impulse. What is the 98% confidence interval for the

A college believes that 28% of applicants to that school have parents who have remarried. How large a sample is needed to estimate the

A sample of 1,108 was used to estimate a proportion with 98% confidence. If p = 0.5, what was the amount of error?

The __________ are the number of values that are free to vary after a sample statistic has been computed. ________________________________________

If a population has standard deviation 18, what is the minimum sample size to be 95% confident that the error should be accurate to within 4?

A random sample of 95 printers discovered that 25 of them were being used in small businesses. Find the 99% limit for the population proportion of printers that are used in small businesses.

$z \alpha / 2$ Which value of was used in the figure below?

In 2000 there were almost 300,000 Canadians with more than 1 million dollars in financial assets! If the average age of one hundred randomly selected millionaires was 54.8 years with a standard deviation of 7.9 years, what is the 95% confidence interval for the mean age, $\mu$ of all Canadian millionaires?

According to Statistics Canada, on July 1, 2006 the population size of the province of Quebec was 7,651,531 whereas Nova Scotia was considerably smaller at 934,405. Thus the margin of error for a Gallup Poll based on a random sample of 1000 Nova Scotians is smaller than that based on a random sample of 1000 Quebeckers.

A study of peach trees showed that the average number of peaches per tree was 1000. The standard deviation of the population is 150. A scientist wishes to find the 98% confidence interval for the mean Number of peaches per tree. How many trees does she need to sample to be accurate within 20 peaches Per tree?

What is the value for $\chi _ { \text {left } } ^ { 2 }$ for a 98% confidence interval when n = 12?

The __________ is the maximum likely difference between the point estimate of a parameter and the actual value of the parameter.

A lawyer researched the average number of years served by 45 different judges on the Supreme Court. The average number of years served was 13.8 years with a standard deviation of 7.3 years. What is the 95% confidence interval for the average number of years served by all Supreme Court judges?

When computing a confidence interval for a population mean using raw data, round off to two more decimal places than the number of decimal places in the original data.