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 37 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 α = 0.10. (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; right-tailed

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

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

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

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

The normal distribution, since the sample size is large.

The t 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.)

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

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 α?

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

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

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

At the α = 0.10 level, we fail to reject the null hypothesis 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 that the true proportion of driver fatalities related to alcohol is less than 0.77 in Kit Carson County.

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

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

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

Answer 1

Solution :

The level of significance is = 0.10

This is the left tailed test .

The null and alternative hypothesis is

H₀ : p = 0.77

H_a : p < 0.77

= x / n = 37 / 51 = 0.7255

The normal distribution, since the sample size is large.

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.7255 - 0.77 / [(0.77 * 0.23) / 51]

= -0.76

P(z < -0.76) = 0.2236

P-value = 0.2236

= 0.10

P-value >

Fail to reject the null hypothesis .

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

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