The U.S. Department of Transportation, National Highway TrafficSafety Administration, reported that 77% of all fatally injuredautomobile drivers were intoxicated. A random sample of 33 recordsof automobile driver fatalities in Kit Carson County, Colorado,showed that 18 involved an intoxicated driver. Do these dataindicate that the population proportion of driver fatalitiesrelated to alcohol is less than 77% in Kit Carson County? Use? = 0.01. Solve the problem using both the traditionalmethod and the P-value method. Since the samplingdistribution of p? is the normal distribution, you can usecritical values from the standard normal distribution as shown inthe table of critical values of the z distribution. (Roundthe test statistic and the critical value to two decimal places.Round the P-value to four decimal places.)
| test statistic | = | |
| critical value | = | |
| P-value | = | |
State your conclusion in the context of the application.
There is sufficient evidence at the 0.01 level to conclude thatthe true proportion of driver fatalities related to alcohol is lessthan 77%.There is insufficient evidence at the 0.01 level toconclude that the true proportion of driver fatalities related toalcohol is less than 77%.
Compare your conclusion with the conclusion obtained by using theP-value method. Are they the same?
We reject the null hypothesis using the P-value method,but fail to reject using the traditional method.The conclusionsobtained by using both methods are thesame. We reject the null hypothesis usingthe traditional method, but fail to reject using theP-value method.
