Question

The article “Evaluation of Criteria for Setting Speed Limits on Gravel Roads” (S. Dissanayake, Journal of Transportation Engineering, 2011:57–63) measured speeds of vehicles on several roads in the state of Kansas. On South Cedar Niles, 73 vehicles were observed, and 49 of them were exceeding the speed limit. Can you conclude that more than 60% of the vehicles on South Cedar Niles exceed the speed limit?

Answer 1

SOLUTION-

WE ARE TO TEST IF MORE THAN 60% OF THE VEHICLES EXCEED THE SPEED LIMIT. HENCE, THE HYPOTHESIS WE FRAME IS,

WE OBSERVE A RANDOM SAMPLE OF 73 VEHICLES AND SEE THAT 49 OF THEM EXCEEDED SPEED LIMIT.

SO WE PERFORM A ONE SAMPLE PROPORTION TEST WITH LEVEL OF SIGNIFICANCE( =0.05) AND USE MINITAB 16 TO TEST THE ABOVE STATED HYPOTHESIS:

STEPS-

STAT> BASIC STATISTICS> 1 PROPORTIONS> SET THE EVENTS AS 49 AND TRIALS AS 73> UNDER 'OPTIONS', SET CONFIDENCE LEVEL AS 95.0 AND ALTERNATE AS 'GREATER THAN'> OK

OBSERVATIONS-

THE TEST STATISTIC IS, Z=1.24 AND THE CORRESPONDING P-VALUE IS 0.107

CONCLUSION-

AS P-VALUE < LEVEL OF SIGNIFICANCE, WE REJECT THE NULL HYPOTHESIS AND CONCLUDE THAT MORE THAN 60% OF THE VEHICLES EXCEED SPEED LIMITS.

**REMARK**- IN CASE OF DOUBT, COMMENT BELOW. ALSO LIKE THE SOLUTION, IF POSSIBLE.