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 50 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 ? = 0.10.

(a) What is the level of significance?


State the null and alternate hypotheses.

H0: p = 0.77; H1: p > 0.77H0: p = 0.77; H1: p ? 0.77    H0: p < 0.77; H1: p = 0.77H0: 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.

Explanation / Answer

The statistical software output for this problem is:

One sample proportion summary hypothesis test:
p : Proportion of successes
H0 : p = 0.77
HA : p < 0.77

Hypothesis test results:

Hence,

a) Level of significance = 0.10

Hypotheses: H0: p = 0.77; H1: p < 0.77

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

Option D is correct.

Sample test statistic = -1.51

c) P - value = 0.0652

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