Question Help In 1945, an organization surveyed 1100 adults and asked, \"Are you

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Question Help In 1945, an organization surveyed 1100 adults and asked, "Are you a total abstainer from, or do you on occasion consume, alcoholic beverages?" of the 1100 adults surveyed, 374 indicated that they wem total abstainers. In a recent survey, the same question was asked of 1100 adults and 308 indicated that they were total abstainers. Complete parts (a) and (b) below (a) Determine the sample proportion for each sample The proportions of the adults who took the 1945 survey and the recent survey who were to al a stainers are and respectively (Round to three decimal places as needed.) (b) Has the proportion of adults who totally abstain from alcohol changed? Use the :0 05 level of significance First verify the model requirements. Select all that apply n,p (1-P)10 and n2p2 (1-2) 10 B. The samples are independent c. The sample size is more than 5% of the population size for each sample, D. The sample size is less than 5% of the population size for each sample E. The data come from a population that is normally distributed. The samples are dependent identify the null and alternative hypotheses for this test Let pt represent the population proportion of 194 who were total abstainers 5 adults who were total abstainers and p2 represent the population proportion of recent Determine the null and alternative hypotheses Click to select your answer(s). Search Windows

Explanation / Answer

a.
sample one, x1 =374, n1 =1100, p1= x1/n1=0.34
sample two, x2 =308, n2 =1100, p2= x2/n2=0.28

b.
data comes from population are normally distributed

Given that,
sample one, x1 =374, n1 =1100, p1= x1/n1=0.34
sample two, x2 =308, n2 =1100, p2= x2/n2=0.28
null, Ho: p1 = p2
alternate, H1: p1 > p2
level of significance, = 0.05
from standard normal table,right tailed z /2 =1.645
since our test is right-tailed
reject Ho, if zo > 1.645
we use test statistic (z) = (p1-p2)/(p^q^(1/n1+1/n2))
zo =(0.34-0.28)/sqrt((0.31*0.69(1/1100+1/1100))
zo =3.042
| zo | =3.042
critical value
the value of |z | at los 0.05% is 1.645
we got |zo| =3.042 & | z | =1.645
make decision
hence value of | zo | > | z | and here we reject Ho
p-value: right tail - Ha : ( p > 3.0425 ) = 0.00117
hence value of p0.05 > 0.00117,here we reject Ho
ANSWERS
---------------
null, Ho: p1 = p2
alternate, H1: p1 > p2
test statistic: 3.042
critical value: 1.645
decision: reject Ho
p-value: 0.00117 = 0.001

if the population proportions are 0.34,0.28 and one would expect difference in proportion 0.06 the one observed that is about 6 out of 100 repetitions
there is significane evidence that proportion of adults who abstain from alchol totally has changed

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