Question

Problem 2: Speeding in a construction zone

A group of Brigham Young University—Idaho students collected data on the speed of vehicles traveling through a construction zone on a state highway, where the speed was 25 mph. The recorded speed (in mph) of 14 randomly selected vehicles is given below:

20,24,27,28,29,30,32,33,34,36,38,39,40,40

• Assuming speeds are approximately normally distributed, construct a 95% confidence interval for the true mean speed of drivers in this construction zone. Interpret the interval.

• Construct a 99% confidence interval for the true mean speed of drivers in this construction zone. Interpret the interval.

• Compare the widths of the 95% and 99% confidence intervals.

• What conclusions do you draw about the speeds people drive in this construction zone?

Answer 1

= 32.143

s = 6.175

At 95% confidence interval the critical value is t^* = 2.160

The 95% confidence interval is

+/- t^* * s/

= 32.143 +/- 2.160 * 6.175/

= 32.143 +/- 3.565

= 28.578, 35.708

We are 95% confident that the true mean speed of drivers lies between the confidence boundaries 28.578 and 35.708.

At 99% confidence interval the critical value is t^* = 3.012

The 99% confidence interval is

+/- t^* * s/

= 32.143 +/- 3.012 * 6.175/

= 32.143 +/- 4.971

= 27.172, 37.114

We are 99% confident that the true mean speed of drivers lies between the confidence boundaries 27.172 and 37.114.

We can conclude that the speeds of people drive in this construction zone is greater than 25 mph.