Question

The Arizona Highway Patrol wants to estimate what proportion of all drivers exceed the 75 mph speed limit on a stretch of Rt. 40 on the Arizona side of the state border with New Mexico. For a sample of 1000 vehicles on a given day, 413 exceeded the speed limit. Based on this sample, construct a 95% confidence interval for the percent of vehicles that exceed the speed limit.

Answer 1

n = sample size = 1000 ( total number of vehicles )

x = number of vehicle who exceeded speed limit = 413

Formula for confidence interval

E = margin of error

Z_c= Z critical value for given level of confidence

C = 0.95 ( we converted 95 % in to decimal )

Area = 0.9750

We look for the area 0.9750 inside the body of the table to calculate the z critical value.

We get Z critical value as 1.96

Z_c = 1.96

95% confidence interval for the percent of vehicles that exceed the speed limit.

We convert the given confidence interval into percentage.

Final answer

95% confidence interval for the percent of vehicles that exceed the speed limit.

Note if you have Ti - 83 or Ti - 84 calculator

Then follow the path to find the above confidence interval.

Press " STAT " .......> then select " tests " ........> scroll down then select " 1 prop z int "

x = 413

n = 1000

c - level = 0.95

and then press " enter "

Now convert that confidence interval into percentage.

I hope this will help you :)