Question

Problem 2: Speeding in a construction zone Please type the answer. Thank you.

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

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?

Answer 1

solution:-

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

mean = 32.1429

standard deviation = 6.1751

degree of freedom df = n - 1 = 14 - 1 = 13

=> 95% confidence interval

we look into t table with df = 13 and with 95% confidence

critical value t = 2.160

confidence interval formula

mean +/- t * standard deviation/sqrt(n)

32.1429 +/- 2.160 * 6.1751/sqrt(14)

(28.5781 , 35.7077) (rounded to four decimals)

=> 99% confidence interval

we look into t table with df = 13 and with 99% confidence

critical value t = 3.012

confidence interval formula

mean +/- t * standard deviation/sqrt(n)

32.1429 +/- 3.012 * 6.1751/sqrt(14)

(27.1720 , 37.1138) (rounded to four decimals)

=> the widths of the 95% and 99% confidence intervals

width = (upper confidence - lower confidence)

width of 95% confidence

(35.7077-28.5781) = 7.1

width of 99% confidence

(37.1138-27.1720) = 9.9

the 99% confidence is wider

=> conclusions do you draw about the speeds people drive in this construction zone

here to believe that the mean speed of drivers in this area exceeds the posted speed limit