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Question #1 (10%)

Question #1 The State Highway Patrol (SHP) periodically samples vehicle speeds at Milepost 92 on Interstate 17. The SHP is concerned about the dispersion of speeds of vehicles sharing the same highway because significant difference in speed is a known cause of accidents. The speeds of a random sample of 16 vehicles are shown below.e Vehicle-I SpeedP Vehiclee-' SpeedP 69 71.1+3 73.5+3 10+3 70.80 74.10 110 64.60 64.40 67 4+3 50 66.30 69.93 68.70 14+3 66.33 69.0+3 15+3 68.3+3 65 70 60 a. Developa confidence interval estimate of the population variance (i.e., the speed varianceofvehiclesat Milepost 92 on Interstate 17). b. Develop a 90% confidence interval estimate of the population standard deviation.e The SHP's policy is to position a patrol car at Milepost 92 on Interstate 17 if the vehicle speed variance at that location is believed to be greater than 6 mph.e c. d. e. State your hypotheses.e Conduct a hypotheses test (witha .10) to determine whether the speed variance for all vehicles passing Milepost 92 exceeds 6 mph. Interpret your result.f-j