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 54 records of automobile driver fatalities in a certain county showed that 36 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 = 0.10.

1. What is the value of the sample test statistic? (Round your answer to two decimal places.)


2. Find the P-value of the test statistic. (Round your answer to four decimal places.)

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H0 : p = 0.77

Ha : p < 0.77

= x / n = 36 / 54 = 0.67

P0 = 0.77

1 - P0 = 1 - 0.77 = 0.23

Test statistic = z =

= - P0 / [P0 * (1 - P0 ) / n]

=0.67 - 0.77 / [(0.77 * 0.23) / 54 ]

Test statistic = z = -1.75

P(z < -1.75)

P-value = 0.0401

= 0.10   

P-value <

Reject the null hypothesis