The U.S. Department of Transportation, National Highway TrafficSafety Administration, reported that 77% of all fatally injuredautomobile drivers were intoxicated. A random sample of 54 recordsof automobile driver fatalities in Kit Carson County, Colorado,showed that 37 involved an intoxicated driver. Do these dataindicate that the population proportion of driver fatalitiesrelated to alcohol is less than 77% in Kit Carson County? Useα = 0.05.

(a) What is the level of significance?

State the null and alternate hypotheses. Will you use aleft-tailed, right-tailed, or two-tailed test?

H_o: p = 0.77;H₁: p > 0.77; right-tailed

H_o: p < 0.77;H₁: p = 0.77;left-tailed    

H_o: p = 0.77;H₁: p < 0.77; left-tailed

H_o: p = 0.77;H₁: p ≠ 0.77; two-tailed

(b) What sampling distribution will you use? Do you think thesample size is sufficiently large?

The normal distribution, since the sample size is large.

The t distribution, since the sample size islarge.    

What is the value of the sample test statistic? (Use 2 decimalplaces.)


(c) Find the P-value of the test statistic. (Use 4 decimalplaces.)

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

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

At the α = 0.05 level, we reject the null hypothesisand conclude the data are not statistically significant.

At the α = 0.05 level, we fail to reject the nullhypothesis and conclude the data are not statisticallysignificant.    

At the α = 0.05 level, we reject the null hypothesisand conclude the data are statistically significant.

At the α = 0.05 level, we fail to reject the nullhypothesis and conclude the data are statistically significant.

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

Reject the null hypothesis, there is sufficient evidence thatthe true proportion of driver fatalities related to alcohol is lessthan 0.77 in Kit Carson County.

Fail to reject the null hypothesis, there is insufficientevidence that the true proportion of driver fatalities related toalcohol is less than 0.77 in Kit Carson County.  

  Fail to reject the null hypothesis, there issufficient evidence that the true proportion of driver fatalitiesrelated to alcohol is less than 0.77 in Kit Carson County.

Reject the null hypothesis, there is insufficient evidence thatthe true proportion of driver fatalities related to alcohol is lessthan 0.77 in Kit Carson County.