The US. Department of Transportation, National Highway Traffic Safety Administra

Question

The US. Department of Transportation, National Highway Traffic Safety Administration reported that 77% of all fatally injured automobile drivers were intoxicated. A random sample of 33 records of automobile driver fatalities in Kit Carson County Colorado, showed that 17 involved an intoxicated driver. Do these data indicate that the population proportion of driver fatalities related to alcohol is less than 77% in Kit Carson County? Use alpha = 0.01. Solve the problem using both the traditional method and the P-value method. Since the sampling distribution of p is the normal distribution, you can use critical values from the standard normal distribution as shown in the table of critical values of the z distribution. (Round the test statistic and the critical value to two 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 that the true proportion of driver fatalities related to alcohol is less than 77%. There is insufficient evidence at the 0.01 level to conclude that the true proportion of driver fatalities related to alcohol less than 77% is less than 77%. Compare your conclusion with the conclusion obtained by using the P-value method. Are they the same? The conclusions obtained by using both methods are the same. We reject the null hypothesis using the P-value method, but fail to reject using the traditional method. We reject the null hypothesis using the traditional method.

Explanation / Answer

The statistical software output for this problem is:

One sample proportion summary hypothesis test:
p : Proportion of successes
H0 : p = 0.77
HA : p < 0.77

Hypothesis test results:

Hence,

Test statistic = -3.48

Critical value = -2.33

p - Value = 0.0003

Sufficient evidence; Option A

Conclusions obtained are same; Option A

Proportion Count Total Sample Prop. Std. Err. Z-Stat P-value p 17 33 0.51515152 0.073257537 -3.4788023 0.0003

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