The Florida Department of Transportation (FDOT) would like to estimate the average speed of vehicles on the Florida Turnpike. The mean speed, in miles per hour, of a random sample of vehicles was found to be 80 miles per hour. The standard deviation of the speeds of all vehicles on the Florida Turnpike is known to be 9 miles per hour.
Find three different confidence intervals - one with sample size 131, one with sample size 246, and one with sample size 409. Assume that the mean of each sample is 80 miles per hour. Notice how the sample size affects the margin of error and the width of the interval.
Report confidence interval solutions using interval notation. Round solutions to two decimal places, if necessary.
When n=131, the margin of error for a 95% confidence interval is given by .
When n=131, a 95% confidence interval is given by .
When n=246, the margin of error for a 95% confidence interval is given by .
When n=246, a 95% confidence interval is given by .
When n=409, the margin of error for a 95% confidence interval is given by .
When n=409, a 95% confidence interval is given by