Question

_____ According to the National Highway and Traffic Safety Administration, the proportion of fatal traffic accidents in the U.S. in which the driver had a positive blood alcohol concentration (BAC) is 0.36. Suppose a random sample of 105 traffic fatalities in the state of Hawaii results in 41 that involved a positive BAC. Does the sample evidence suggest that Hawaii has a higher proportion of traffic fatalities involving a positive BAC than the general U.S.? Test at the 0.05 level of significance.

a) What are the observational units?

b) What is the variable? Confirm that it is binary/dichotomous.

c) What is the sample estimate of the proportion of fatalities in Hawaii that involved a positive BAC?

d) What is the appropriate critical value to use?

e) Verify that the conditions/requirements are met for conducting the test of hypothesis.

f) State the null and alternative hypotheses.

g) Find the test statistic.

h) Find the p-value.

i) Compare the p-value to the significance level. Do you reject the null?

j) State your conclusion in words in the context of the problem.

Answer 1

a)

observational units is traffic fatalities

b)
Sample proportion = 41/105 = 0.3905

c)
Critical value = 1.645

d)

The conditions are that np0 and n(1-p0) are at least 5

e)

H0 : p0 = 0.36
Ha: p0 > 0.36

f)

z = ( p -p0)/sqrt(p0 *(1-p0)/n)
= (0.3905 - 0.36) /sqrt(0.36 *(1-0.36)/105)
= 0.6511

g)
p value = .2575

h)
No

i)
There is not sufficient evidence to support the claim that Hawaii has a higher proportion of traffic fatalities involving a positive BAC than the general U.S