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 26 records of automobile driver fatalities in Kit Carson County, Colorado, showed that 14 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

H0: p = 0.77

HA: p < 0.77

Sample proportion = 14 / 26 = 0.5385

Test statistics

z = ( - p) / sqrt ( p(1 - p) / n)

= ( 0.5385 - 0.77) / sqrt ( 0.77 * ( 1 - 0.77) / 26)

= -2.80

Critical value at 0.01 significance level = -2.33

Since test statistics z < -2.33 , Reject H0.

p-value = P(Z < z)

= P(Z < -2.80)

= 0.0026

Since p-value < 0.01 significance level, reject H0.

We conclude at 0.01 level that we have sufficient evidence to support the claim that the population proportion of

driver fatalities related to alcohol is less than 77% in Kit Carson County.