Question

The U.S. Department of Transportation, National Highway Traffic Safety Administration, reported that 77% of all fatally...

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 53 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 = 0.01.

(a) What is the level of significance?


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 standard normal, 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.


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 = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.

At the α = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.    

At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

At the α = 0.01 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.

There is sufficient evidence at the 0.01 level to conclude that the true proportion of driver fatalities related to alcohol in the county is less than 0.77.

There is insufficient evidence at the 0.01 level to conclude that the true proportion of driver fatalities related to alcohol in the county is less than 0.77.

Homework Answers

Answer #1

The statistical software output for this problem is :

(a)

Level of significance = 0.01

Option D is correct .

(b)

Option D is correct.

Test statistics = -2.55

(c)

P-value = 0.0054

(d) Option A is correct.

(e) Option A is correct.

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
The U.S. Department of Transportation, National Highway Traffic Safety Administration, reported that 77% of all fatally...
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 53 records of automobile driver fatalities in a certain county showed that 35 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 = 0.05. a) What is the level of significance? State the null and alternate...
The U.S. Department of Transportation, National Highway Traffic Safety Administration, reported that 77% of all fatally...
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...
The U.S. Department of Transportation, National Highway Traffic Safety Administration, reported that 77% of all fatally...
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...
The U.S. Department of Transportation, National Highway Traffic Safety Administration, reported that 77% of all fatally...
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 14 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 = 0.01. Solve the problem using both the traditional method and the P-value...
The U.S. Department of Transportation, National Highway Traffic Safety Administration, reported that 77% of all fatally...
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 25 records of automobile driver fatalities in Kit Carson County, Colorado, showed that 14 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 = 0.01. Solve the problem using both the traditional method and the P-value...
The U.S. Department of Transportation, National Highway Traffic Safety Administration, reported that 77% of all fatally...
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 35 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 = 0.05. (a) What is the level of significance? State the null and alternate...
the U.S. department of transportation, national highway traffic safety administration, reported that 77% of all fatally...
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...
USA Today reported that about 47% of the general consumer population in the United States is...
USA Today reported that about 47% of the general consumer population in the United States is loyal to the automobile manufacturer of their choice. Suppose Chevrolet did a study of a random sample of 1006 Chevrolet owners and found that 488 said they would buy another Chevrolet. Does this indicate that the population proportion of consumers loyal to Chevrolet is more than 47%? Use α = 0.01. (a) State the null and alternate hypotheses. (Pick one) H0: p = 0.47;...
USA Today reported that about 47% of the general consumer population in the United States is...
USA Today reported that about 47% of the general consumer population in the United States is loyal to the automobile manufacturer of their choice. Suppose Chevrolet did a study of a random sample of 1004 Chevrolet owners and found that 482 said they would buy another Chevrolet. Does this indicate that the population proportion of consumers loyal to Chevrolet is more than 47%? Use α = 0.01. (a) What is the level of significance? State the null and alternate hypotheses....
USA Today reported that about 47% of the general consumer population in the United States is...
USA Today reported that about 47% of the general consumer population in the United States is loyal to the automobile manufacturer of their choice. Suppose Chevrolet did a study of a random sample of 1001 Chevrolet owners and found that 483 said they would buy another Chevrolet. Does this indicate that the population proportion of consumers loyal to Chevrolet is more than 47%? Use α = 0.01. (a) What is the level of significance? State the null and alternate hypotheses....