Confidence Intervals for Large Sample Means

Which of the following changes to a study would result in a narrower confidence interval?

• increasing the confidence level or increasing the sample size

• decreasing the confidence level or decreasing the sample size

• increasing the confidence level or decreasing the sample size

• decreasing the confidence level or increasing the sample size.

A lawyer researched the average number of years served by 45 different justices 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 justices? 

• (11.7, 15.9)
• (11.8, 15.8)
• (12.9, 16.9)
• (12.5, 17.3)

An economics professor randomly selected 100 millionaires in the United States.  The average age of these millionaires was 54.8 years with a standard deviation of 7.9 years.  What is the 95% confidence interval for the mean age of all United States millionaires? 

• (53.5, 56.1)
• (53.3, 56.3)
• (52.8, 56.8)
• (51.7, 57.7)

The average number of miles that 90 truckers drove in a day was 540 with a standard deviation of 40 miles.  What is the 99% confidence interval of the true mean number of miles driven by all truckers?

• (496.2, 525.7)
• (529.1, 550.9)
• (563.4, 589.3)
• (289.4, 325.6)

Jennifer wants to find a 95% confidence interval for the time it takes her to get to work.  She kept records for 30 days and found her average time to commute to work was 20.5 minutes with a standard deviation of 3.9 minutes.  Jennifer's maximum error of estimate would be 1.4 minutes.

• True
• False