Question

According to a certain government agency for a large​ country, the proportion of fatal traffic accidents in the country in which the driver had a positive blood alcohol concentration​ (BAC) is

0.37

Suppose a random sample of

110

traffic fatalities in a certain region results in

51

that involved a positive BAC. Does the sample evidence suggest that the region has a higher proportion of traffic fatalities involving a positive BAC than the country at the

alpha equals 0.01α=0.01

level of​ significance?

Answer 1

Solution:

1)

The null and alternative hypothesis are

H₀ : p = 0.37 vs H_a : p > 0.37

2)

n = 110

x = 51

Let   be the sample proportion.

= x/n = 51/110 = 0.4636

The test statistic z is

z =   

=  (0.4636 - 0.37)/[0.37*(1 - 0.37)/110]

= 2.03

Test Statistic z = 2.03

3)

sign in Ha indicates that the test is "RIGHT TAILED"

For right tailed z test ,

p value = P(Z > z) = P(Z > 2.03) = 1 - P(Z < 2.03) = 1 -0.9788 = 0.0212

p value = 0.0212

4)

Decision :

p value is greater than given significance level α = 0.01

Fail to reject the null hypothesis H₀

5)

Conclusion:

There is not sufficient evidence to support the claim that the region has a higher proportion of traffic fatalities involving a positive BAC than the country .