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 52 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 α = 0.10.

(a) What is the level of significance?
Answer: 0.10

State the null and alternate hypotheses.

H₀: p = 0.77; H₁: p < 0.77

H₀: p = 0.77; H₁: p ≠ 0.77

H₀: p = 0.77; H₁: p > 0.77

H₀: p < 0.77; H₁: p = 0.77

(b) What sampling distribution will you use?

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

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

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

The standard normal, since np < 5 and nq < 5.

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

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

Sketch the sampling distribution and show the area corresponding to the P-value.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

At the α = 0.10 level, we reject the null hypothesis and conclude the data are statistically significant.

At the α = 0.10 level, we reject the null hypothesis and conclude the data are not statistically significant.    

At the α = 0.10 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

At the α = 0.10 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

(e) Interpret your conclusion in the context of the application.

Answer:

There is sufficient evidence at the 0.10 level to conclude that the true proportion of driver fatalities related to alcohol in the county is less than 0.77.

Answer 1