Question

21.) 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 (BAC) is .38. suppose a random sample of 108 traffic fatalities in a certain region results in 52 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=.05 level of significance?

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 loohol concentration (BAC) 0.38. Suppose a random sample of 100 vull faltes in certain region results in 52 that involved a positive BAG. Does the sample evidence suggest that the region has a higher proportion of trade falfies involving positive BAC than the country at the -0.05 level of significance? Because no (1-) - 10, the sample size is 5% of the populations, and the sample the requirements for testing the hypothesia {Round to one deimal place as needed.) What are the land tomative hypothese? versus H, (Type integers or decimal. Do not round.) Find the best statistico 1o-Round to two decimal places as needed) Find the value P.valueRound to three decimal places as needed) Determine the conclusion for this hypothesis test. Choose the correct answer below O A. Since P-value <a, reject the rul hypothesis and conclude that there is sufficient evidence that the region has a higher proportion of traffic stalties involving a positive BAC than the country O B. Since P.Value, do not reject the null hypothesis and conclude that there is not sufficient evidence that the region has a higher proportion of traffic futairies involving a positive BC than the country OC. Since P value <a, do not reject the null hypothesis and conclude that there is not contevidence that the region has a higher proportion of traficulties involving a positive BAC than the country OD Since value reject the rol hypothesis and conclude that there is suficient evidence that the region has a higher proportion of traffic talities involving a positive BAC than the country

Answer 1

n = 108

x = 52

p =0.38

$\hat{p}=\frac{x}{n}=\frac{52}{108}=0.4815$

np(1-p) = 25.4448

Becuase of $np_0(1-p_0)$ = 25.4 > 10 , the sample size less than 5% of the population size, and the sample can be resonably assumed to be random the requirement of hypothesis testing are satisfied.

Hypothesis :

Test Statistics

$Z_0 =\frac{\hat{p}-p}{\sqrt{\frac{p*(1-p)}{n}}}$

$Z_0 =\frac{0.4815-0.38}{\sqrt{\frac{0.38*(1-0.38)}{108}}}$

$Z_0 =\frac{0.1015}{\sqrt{\frac{0.2356}{108}}}$

$Z_0 =\frac{0.1015}{\sqrt{0.002181481}}$

$Z_0 =\frac{0.1015}{0.046706332}$

Z0 = 2.17      ( rounded )

P value : 0.015

( To get p value check 2.17 in Z table we get 0.9850 subtract this value from 1or use excel command = 1-NORMSDIST(2.17) )

Conclusion : A

P value < $\alpha$ , reject null hypothesis and conclude that there is sufficient evidence the region has a higher proportion of traffic fatalities involving a positive BAC than the country .