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 29 records of automobile driver fatalities in kit Carson county, Colorado, showed that 15 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 level of significance =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. round the p- value to four decimal places.)

Answer 1

Claim:  The population proportion of driver fatalities related to alcohol is less than 77% in kit Carson county.

The null and alternative hypothesis is

H0: P = 0.77

H1: P < 0.77

Level of significance = 0.01

Sample size = n = 29

x = 15

Test statistic is

Traditional method:

Critical value = 2.32

( From z table)

Test statistic | z | > 2.32 we reject null hypothesis.

P-value method:

P-value = P(Z < -3.23) = 0.0006

P-value < 0.01 we reject null hypothesis.

Conclusion:

The population proportion of driver fatalities related to alcohol is less than 77% in kit Carson county.