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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 a = 0.05.

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 a = 0.05.

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter11: Data Analysis And Probability
Section: Chapter Questions
Problem 8CR
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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 a = 0.05. A USE SALT (a) What is the level of significance? .05 State the null and alternate hypotheses. O Ho: P = 0.77; H: p> 0.77 • Ho:P = 0.77; H: p< 0.77 O H: p = 0.77: H,: p 0.77 O H,: P< 0.77; H,: p = 0.77 (b) What sampling distribution will you use? O The standard normal, since np < 5 and ng < 5. The Student's t, since np < 5 and ng < 5. O The Student's t, since np > 5 and ng > 5. O The standard normal, since np > 5 and ng > 5. What is the value of the sample test statistic? (Round your answer to two decimal places.)
Transcribed Image Text: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 a = 0.05. A USE SALT (a) What is the level of significance? .05 State the null and alternate hypotheses. O Ho: P = 0.77; H: p> 0.77 • Ho:P = 0.77; H: p< 0.77 O H: p = 0.77: H,: p 0.77 O H,: P< 0.77; H,: p = 0.77 (b) What sampling distribution will you use? O The standard normal, since np < 5 and ng < 5. The Student's t, since np < 5 and ng < 5. O The Student's t, since np > 5 and ng > 5. O The standard normal, since np > 5 and ng > 5. What is the value of the sample test statistic? (Round your answer to two decimal places.)
(b) What sampling distribution will you use? O The standard normal, since np < 5 and nq < 5. The Student's t, since np < 5 and nq < 5. O The Student's t, since np > 5 and nq > 5. O 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.
Transcribed Image Text:(b) What sampling distribution will you use? O The standard normal, since np < 5 and nq < 5. The Student's t, since np < 5 and nq < 5. O The Student's t, since np > 5 and nq > 5. O 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.
Expert Solution
Step 1

Given Information:

Proportion p=0.77

Sample size n=50

Out of which x=33 records involved an intoxicated driver.

Claim: Population proportion of driver fatalities related to alcohol is less than 77%.

Significance level α=0.05

 

(b) Since, np>5 i.e., 500.77=38.5>5 and nq>5 i.e.,  nq=n1-p=501-0.77=11.5>5

We use standard normal distribution.

 

Sample proportion is the number of successes divided by the sample size. It is given by the formula p^=xn

So, sample proportion is:

p^=3350=0.66

 

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