The U.S. Department of Transportation, National Highway Traffic Safety Administr

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 51 records of automobile driver fatalities in a certain county showed that 34 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 a = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. H_0: rho = 0.77; H_1: rho > 0.77 H_0: rho = 0.77; H_1: rho 5. The standard normal since np > 5 and nq > 5. The Student's t, since np

Explanation / Answer

Solution:

a) What is the leval of significance
The probability of rejecting the null hypothesis in a statistical test when it is true is called level of significance
H0: p = 0.77; H1:p < 0.77

b) The number of trails is n = 51 and the number of successes is r = 8. Thus,
p = r/n
= 34/51
= 0.6667
From H0, p = 0.77 and q = 1-p = 0.33
Then, np = 51(0.77) = 39.27 > 5
n1 = 51(0.33) = 16.83 > 5
So, we can use the normal distribution for p
test statistic z = p-p/sqrt(pq/n)
= (0.6667 - 0.77)/sqrt((0.77*0.33)/51)
= -1.4634
c) P-value = 2P(Z< -1.4634)
= 2(0.0717) = 0.1434
Sicne, P-value 0.1434 > 0.05, we fail to reject H0 and conclude the data are statistically significant.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.