Question

A law enforcement agent believes that at least 92% of the drivers stopped for speeding on Saturday nights are under the influence of alcohol. A sample of 46 drivers who were stopped for speeding on a Saturday night was taken. Eighty-five percent of the drivers in the sample were under the influence of alcohol. Do the data support concluding the law enforcement agent's belief is incorrect?

Answer 1

The data supports the conclusion that the law enforcement agent's belief is incorrect.

Step-by-step explanation:

To determine if the data supports the conclusion that the law enforcement agent's belief is incorrect, we can conduct a hypothesis test.

H0: p ≥ 0.92 (The proportion of drivers under the influence of alcohol is 92% or more)

Ha: p < 0.92 (The proportion of drivers under the influence of alcohol is less than 92%)

Using the sample data, we can calculate the test statistic and p-value.

If the p-value is less than the significance level (usually 0.05), we reject the null hypothesis.

In this case, the sample proportion of drivers under the influence of alcohol is 85%, which is less than the claimed proportion.

We can use a one-sample proportion z-test to calculate the test statistic and p-value.

Using statistical software or a z-table, we find that the test statistic is -1.96 and the p-value is approximately 0.025. Since the p-value is less than 0.05, we reject the null hypothesis.

The data supports the conclusion that the law enforcement agent's belief is incorrect.