A law enforcement agent believes that at least 90 of the dri

A law enforcement agent believes that at least 90% of the drivers stopped on Saturday nights for speeding are under the influence of alcohol. A sample of 100 drivers who were stopped for speeding on a Saturday night was taken and 87% of the drivers in the sample were under the influence of alcohol. Showing all steps, at 99% 1. confidence level develop and test this hypothesis and make a conclusion.

Solution

ANSWER:

H0 : P > = 0.9

H1 : P < 0.9

Sample proportion p hat = 0.87

variance of propotion = p * ( 1 - p) / n

n =100

variance = 0.9 * ( 1 - 0.9) / 100

variance = 0.9 * 0.1 / 100

variance = 0.09 / 100 = 0.0009

std = (variance) ^ 1/2 = (0.0009) ^ 1/2 = 0.03

z value = (p hat - p) / std

z value = (0.87 - 0.9) / 0.03

z value = -0.03 / 0.03 = -1

p value (z < -1) = 0.1587

since 0.1587 > 0.01 (99% confidence level) , we accept the null hypothesis and conclude that more then 90% of the drivers are under the influence of alcohol on saturday nights.