The U.S. Department of Transportation, National Highway Traffic Safety Administration, reported that 75% of all fatally injured automobile drivers were intoxicated. A random sample of 52 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 75% in Kit Carson County? Use ? = 0.10.

(a)

What is the level of significance?

State the null hypothesis
H₀
and the alternate hypothesis
H₁
.

H₀
: p

H₁
: p

(b)

What sampling distribution will you use?
The Student's tThe standard normal
since np

and nq

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.

A plot of the standard normal probability curve has a horizontal axis with values from −3 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 1.92 and 3 is shaded.

A plot of the standard normal probability curve has a horizontal axis with values from −3 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 −1.92 and 3 is shaded.

A plot of the standard normal probability curve has a horizontal axis with values from −3 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 −3 and −1.92 as well as the area under the curve between 1.92 and 3 are both shaded.

A plot of the standard normal probability curve has a horizontal axis with values from −3 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 −3 and −1.92 is shaded.
graph!!

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.

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 75%.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 75%.

Question

The U.S. Department of Transportation, National Highway Traffic Safety Administration, reported that 75% of all fatally injured automobile drivers were intoxicated. A random sample of 52 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 75% in Kit Carson County? Use ? = 0.10.

(a)

What is the level of significance?

State the null hypothesis

H₀

and the alternate hypothesis

H₁

.

H₀

: p

H₁

: p

(b)

What sampling distribution will you use?

The Student's tThe standard normal

since np

and nq

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.

A plot of the standard normal probability curve has a horizontal axis with values from −3 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 1.92 and 3 is shaded.

A plot of the standard normal probability curve has a horizontal axis with values from −3 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 −1.92 and 3 is shaded.

A plot of the standard normal probability curve has a horizontal axis with values from −3 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 −3 and −1.92 as well as the area under the curve between 1.92 and 3 are both shaded.

A plot of the standard normal probability curve has a horizontal axis with values from −3 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 −3 and −1.92 is shaded.

graph!!

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.

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 75%.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 75%.

Accepted Answer

Answered: Image /qna-images/answer/e988e84c-50c3-4738-9c14-ae639b4421f7.jpg