Problem 2: Speeding in a construction zone

A group of Brigham Young UniversityIdaho 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

1. 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.
2. Construct a 99% confidence interval for the true mean speed of drivers in this construction zone. Interpret the interval.
3. Compare the widths of the 95% and 99% confidence intervals.
4. What conclusions do you draw about the speeds people drive in this construction zone?