Question

On New Year’s Eve, Police set up a sobriety checkpoint at which drivers were stopped. The police did a visual check to see if the driver was impaired. They found that there was probable cause to inspect 12 of the 225 vehicles stopped.

a)Find a 95% confidence interval for the proportion of drivers in the county that have their cars inspected at a sobriety checkpoint. Do not make these calculations by hand. Instead, use the 1-PropZInt command in your graphing calculator found under STAT –TESTS. Write out what you entered in your calculator. (4points)

b)Use your interval to find the margin of error associated with this confidence interval. (2points)

c)Interpret your interval above in the context of this problem. (2points)

Answer 1

Solution:

Given:

n = 225

x = 12

confidence level = c = 95%

Part a)

Use following steps in TI 84 plus calculator:

Press STAT and select TESTS

Under TESTS select 1 PropZInt

Enter numbers:

Click on Calculate and press Enter

Lower Bound = 0.02397 = 0.0240

Upper Bound = 0.08269 = 0.0827

_{(Round final answer to specified number of decimal places)}

A 95% confidence interval for the proportion of drivers in the county that have their cars inspected at a sobriety checkpoint is between 0.0240 and 0.0827.

Part b) Margin of Error E:

_{(Round final answer to specified number of decimal places)}

Part c) Interpret your interval above in the context of this problem.

We are 95% confident that the true proportion of drivers in the county that have their cars inspected at a sobriety checkpoint is between 0.0240 and 0.0827.