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 50 records of automobile driver fatalities in a certain county showed that 33 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.

a) what is the level of significance?

State the null and alternate hypotheses

b) what sampling distribution will you use?

A. the standard normal since, np<5 and nq>5

B. The Student's t, since np > 5 and nq > 5.

C. The standard normal, since np > 5 and nq > 5

D. The Student's t, since np < 5 and nq < 5

What is the value of the sample test statistic?

c) Find the P-value of the test statistic

Answer 1

Solution :

This hypothesis test is a less tailed test .

The null and alternative hypothesis is

H₀ : p =0.77

H_a : p < 0.77

= x / n = 33 / 50 = 0.66

C. The standard normal, since np > 5 and nq > 5

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.66 - 0.77 / [(0.77 * 0.23) / 50]

Test statistic = -1.848

P-value = 0.0323