Question

The U.S. Department of Transportation, National Highway Traffic Safety Administration, reported that 77% of all fatally injured automobile drivers were intoxicated. A random sample of 34 records of automobile driver fatalities in Kit Carson County, Colorado, showed that 19 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 α = 0.01. Solve the problem using both the traditional method and the P-value method. Since the sampling distribution of p̂ 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. Round the P-value to four decimal places.)

test statistic =

critical value =

P-value =

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 0.559

This a left (One) tailed test.

The null and alternative hypothesis is,

Ho: p = 0.77

Ha: p < 0.77

Test statistics

z = ( - ) / *(1-) / n

= ( 0.559 - 0.77) / (0.77*0.23) / 34

= -2.92

Critical value of  the significance level is α = 0.01, and the critical value for a left-tailed test is

= -2.33

P-value = P(Z < -2.92 )

= 0.0018

The p-value is p = 0.0018, and since p = 0.0018 < 0.01, it is concluded that the null hypothesis is rejected.