According to a certain government agency for a large country, the proportion of

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 0.38. Suppose a random sample of 107 traffic fatalities in a certain region results in 53 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 = 0.05 level of significance?

This Question: 14 pts This Test: 100 pts possible Show Work! Question Help * 4 of 14 (2 complete) l4 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 107 traffic fatalities in a certain region results in 53 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 : 0.05 level of significance? Because nPo (1-Po) = | | | > 10, the sample size is | less than | 5% of the population size, and the sample is given to be random, the requirements for testing the hypothesis are not satisfied (Round to one decimal place as needed.) What are the null and alternative hypotheses? (Type integers or decimals. Do not round.) Find the test statistic, zo- ZoRound to two decimal places as needed.) Find the P-value P-value = | | (Round to three decimal places as needed.) Determine the conclusion for this hypothesis test. Choose the correct answer below. 0 A. 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 fatalities involving a positive RAC than the country

Explanation / Answer

Given that,
possibile chances (x)=53
sample size(n)=107
success rate ( p )= x/n = 0.4953
success probability,( po )=0.38
failure probability,( qo) = 0.62
null, Ho:p=0.38  
alternate, H1: p>0.38
level of significance, = 0.05
from standard normal table,right tailed z /2 =1.64
since our test is right-tailed
reject Ho, if zo > 1.64
we use test statistic z proportion = p-po/sqrt(poqo/n)
zo=0.49533-0.38/(sqrt(0.2356)/107)
zo =2.4577
| zo | =2.4577
critical value
the value of |z | at los 0.05% is 1.64
we got |zo| =2.458 & | z | =1.64
make decision
hence value of | zo | > | z | and here we reject Ho
p-value: right tail - Ha : ( p > 2.45774 ) = 0.00699
hence value of p0.05 > 0.00699,here we reject Ho
ANSWERS
---------------
null, Ho:p=0.38
alternate, H1: p>0.38
test statistic: 2.46
critical value: 1.64
decision: reject Ho
p-value: 0.007
Option C.

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