Question

0.79 of 1 Point 10.2.19-T Question Help 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 0.38. Suppose a random sample of 109 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 a = 0.1 level of significance? Find the test statistic, zo. 1.89 (Round to two decimal places as needed.) Zo %3D Find the P-value. P-value = 0.029° (Round to three decimal places as needed.) Determine the conclusion for this hypothesis test. Choose the correct answer below. GA. Since P-value < a, do not reject the null hypothesis and conclude that there is not sufficient evidence that the region has a hiaher pronortion of traffic fatalities involvina a nositive BAC than the countrv Question is complete. Tap on the red indicators to see incorrect answers.

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H₀ : p = 0.38

H_a : p $\neq$ 0.38

n = 109

x = 51

$\hat p$ = x / n = 51 / 10 9 =0.48

P₀ = 0.38

1 - P₀ = 1 -0.38 = 0.62

Test statistic = z

= $\hat p$ - P₀ / [$\sqrt$P_{0 *} (1 - P₀ ) / n]

= 0.48 - 0.38/ [$\sqrt$0.38 *0.62 / 109]

= 1.89

Test statistic = z = 1.89

P(z >1.89 ) = 1 - P(z < 1.89) = 1 - 0.9706

P-value = 0.029

$\alpha$ = 0.1

P-value < $\alpha$

0.029 < 0.1

Reject the null hypothesis .

There is sufficient evidence to suggest that