The U.S. Department of Transportation, National Highway Traffic Safety Administr
ID: 3325869 • Letter: T
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 Kit Carson County, Colorado, 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 = 0.05.
(a) What is the level of significance?
State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?
Ho: p = 0.77; H1: p < 0.77; left-tailedHo: p = 0.77; H1: p > 0.77; right-tailed Ho: p < 0.77; H1: p = 0.77; left-tailedHo: p = 0.77; H1: p 0.77; two-tailed
(b) What sampling distribution will you use? Do you think the sample size is sufficiently large?
The t distribution, since the sample size is large.The normal distribution, since the sample size is large.
What is the value of the sample test statistic? (Use 2 decimal places.)
(c) Find the P-value of the test statistic. (Use 4 decimal places.)
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,
Hypotheses: Ho: p = 0.77; H1: p < 0.77; left-tailed
The normal distribution, since the sample size is large.
Test statistic = -1.42
P - value = 0.0777
Proportion Count Total Sample Prop. Std. Err. Z-Stat P-value p 35 51 0.68627451 0.058928338 -1.4208018 0.0777Related Questions
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