A local neighborhood has just installed speed bumps to slow

A local neighborhood has just installed speed bumps to slow traffic. Two weeks after the installation the city recorded the following speeds 500 feet after the speed bump: 29,29,31,42,30,24,30,27,33,44,28,32,30,24,35,34,30,23,35,27. DO BY HAND.

a. Find a 99% confidence interval on mean speed thickness and access whether or not the average speed is 25 or less. Assume that the data is normally distributed.

Solution

sample size =n=20

sample mean=30.85

sample standard deviation = 5.382965

The degree of freedom =n-1=20-1=19

Given a=0.01, t(0.005, df=19) =2.86 (from student t table)

So the lower bound is

xbar - t*s/vn =30.85 - 2.86*5.382965/sqrt(20) =27.40751

So the upper bound is

xbar + t*s/vn =30.85 + 2.86*5.382965/sqrt(20)=34.29249

Since all values in the interval are greater than 25, we can not conclude that the average speed is 25