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 of52records of automobile driver fatalities in a certain county showed that35involved 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< 0.77

H₀:p= 0.77;H₁:p> 0.77

H₀:p= 0.77;H₁:p0.77

H₀:p< 0.77;H₁:p= 0.77

(b)What sampling distribution will you use?

The standard normal, sincenp> 5 andnq> 5.

The Student'st, sincenp< 5 andnq< 5.

The Student'st, sincenp> 5 andnq> 5.

The standard normal, sincenp< 5 andnq< 5.

What is the value of the sample test statistic? (Round your answer to two decimal places.)

(c)Find theP-value of the test statistic. (Round your answer to four decimal places.)

Sketch the sampling distribution and show the area corresponding to theP-value.

A plot of the standard normal probability curve has a horizontal axis with values from3 to 3. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between 1.66 and 3 is shaded

A plot of the standard normal probability curve has a horizontal axis with values from3 to 3. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between3 and1.66 as well as the area under the curve between 1.66 and 3 are both shaded.

A plot of the standard normal probability curve has a horizontal axis with values from3 to 3. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between1.66 and 3 is shaded.

A plot of the standard normal probability curve has a horizontal axis with values from3 to 3. The curve enters the window from the left, just above the horizontal axis, goes up and to the right, changes direction over approximately 0 on the horizontal axis, and then goes down and to the right before exiting the window just above the horizontal axis. The area under the curve between3 and1.66 is shaded.

(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?

At the= 0.10 level, we reject the null hypothesis and conclude the data are statistically significant.

At the= 0.10 level, we reject the null hypothesis and conclude the data are not statistically significant.

At the= 0.10 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

At the= 0.10 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 0.10 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 0.10 level to conclude that the true proportion of driver fatalities related to alcohol in the county is less than 0.77.