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 54 records of automobile driver fatalities in a certain county 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 α = 0.05.

(a) What is the level of significance?

State the null and alternate hypotheses.

(b) What sampling distribution will you use?

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.)

(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?

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

Answer 1

a)

H0: p = 0.77

Ha: p < 0.77

Level of significance = 0.05

b)

We use sampling distribution of sample proportion (One proportion z test)

Sample proportion = 35 / 54 = 0.6481

Test statistics

z = ( - p) / Sqrt [ p( 1 - p) / n ]

= (0.6481 - 0.77 ) / sqrt [ 0.77 * ( 1 - 0.77) / 54]

= -2.13

c)

p-value = P(Z < z)

= P(Z < -2.13)

= 0.0166

d)

Since p-value < 0.05 level, reject the null hypothesis.

Data is statistically significant at level

e)

We conclude at 0.05 level that we have sufficient evidence to support the claim.