SOLUTION: In some states, the law requires drivers to turn on their headlights when driving in the rain. A highway patrol officer believes that less than one-quarter of all drivers follow th

Algebra ->  Probability-and-statistics -> SOLUTION: In some states, the law requires drivers to turn on their headlights when driving in the rain. A highway patrol officer believes that less than one-quarter of all drivers follow th      Log On


   

Question 923897: In some states, the law requires drivers to turn on their headlights when driving in the rain. A highway patrol officer believes that less than one-quarter of all drivers follow this rule. As a test, he randomly samples 200 cars driving in the rain and counts the number whose headlights are turned on. His finds this number to be 41. Does the officer have enough evidence at the 10% significance level to support his belief?
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
Ho: p = 0.25
Ha: p< 0.25 (officer claim)
....
sample proportion = p-hat = 40/200 = 0.205
....
test stat: z(.205) = -.045/sqrt(.25*.75/200) = - .045/.0306 = -1.47
...
P( z < -1.47) = normalcdf(-100, -1.47) = .0708
...
.07 < .10 (reject Ho)
officer has enough evidence at the 10% significance level to support his claim