Question

According to the National Institute on Alcohol Abuse and Alcoholism (NIAAA), and the National Institutes of Health (NIH), 41% of college students nationwide engage in “binge drinking” behavior, having 5 or more drinks in one occasion during the past two weeks. A college president wonders if the proportion of students enrolled at her college that binge drink is actually different than the national proportion.

In a commissioned study, 348 students are selected randomly from a list of all students enrolled at the college. Of these, 118 admitted to having engaged in binge drinking.

1. Identify the variable of interest – be specific. Then calculate the statistic and standard error for a CI for this sample.

Answer 1

a.
Given that,
possibile chances (x)=118
sample size(n)=348
success rate ( p )= x/n = 0.339
success probability,( po )=0.41
failure probability,( qo) = 0.59
null, Ho:p=0.41
alternate, H1: p!=0.41
level of significance, α = 0.05
from standard normal table, two tailed z α/2 =1.96
since our test is two-tailed
reject Ho, if zo < -1.96 OR if zo > 1.96
we use test statistic z proportion = p-po/sqrt(poqo/n)
zo=0.33908-0.41/(sqrt(0.2419)/348)
zo =-2.69
| zo | =2.69
critical value
the value of |z α| at los 0.05% is 1.96
we got |zo| =2.69 & | z α | =1.96
make decision
hence value of | zo | > | z α| and here we reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != -2.68991 ) = 0.00715
hence value of p0.05 > 0.0071,here we reject Ho
ANSWERS
---------------
Z test for proportion is used
null, Ho:p=0.41
alternate, H1: p!=0.41
test statistic: -2.69
critical value: -1.96 , 1.96
decision: reject Ho
p-value: 0.00715
we have enough evidence to support the claim that if the proportion of students enrolled at her college that binge drink is actually different than the national proportion.
given that,
possible chances (x)=118
sample size(n)=348
success rate ( p )= x/n = 0.339
where,
Za/2 = Z-table value
level of significance, α = 0.05
from standard normal table, two tailed z α/2 =1.96
I.
sample proportion = 0.339
standard error = Sqrt ( (0.339*0.661) /348) )
= 0.025