Question

The sheriff is concerned about speedsters on a certain stretch of county road. The sheriff, a retired statistician, sets up a radar device and, over a long period of time, obtains data on the entire population of vehicles using the road. The mean vehicle speed: 50 miles per hour.

A skeptical county commissioner claims that the crackdown had no effect and that average speed on the roadway is still 50 mph. (i) Is the skeptic on solid statistical ground? (ii) Explain how you know.

Answer 1

I think you missed this information in the question:

"The sheriff cracks down on speeders. Following the crackdown, the sheriff takes a random sample (n=100) of vehicle speeds on the roadway. The sample data: sample mean, 47 mph; sample deviation, 8 mph."

If yes, solution is as follows:

n = 100

= 47

s = 8

H0: = 50

H1: < 50

Since we don't know the population std. deviation, we will use t-test.

df = n-1

= 99

p-value = 0.0001 < 0.05 (significance level) i.e. we can reject H0 and hence we can say that claims of the county commissioner is not right as the speed has decreased.

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