Question

The Current method for 100% detection of contraband passing through X-Ray screeners by TSA agents in the United is 14%. We develop a new way that teaches screeners to use different color schemes to illuminate items such that a person can see the items in the color scheme that makes sense to them. Out of the 24 TSA agents that volunteered to participate in a program, 8 were now capable of 100% detection. Perform an appropriate hypothesis test to determine if this is significantly different than the prior estimate.

Answer 1

Given that,
possible chances (x)=8
sample size(n)=24
success rate ( p )= x/n = 0.333
success probability,( po )=0.14
failure probability,( qo) = 0.86
null, Ho:p=0.14
alternate, H1: p!=0.14
level of significance, alpha = 0.05
from standard normal table, two tailed z alpha/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=0.33333-0.14/(sqrt(0.1204)/24)
zo =2.73
| zo | =2.73
critical value
the value of |z alpha| at los 0.05% is 1.96
we got |zo| =2.73 & | z alpha | =1.96
make decision
hence value of | zo | > | z alpha| and here we reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != 2.7296 ) = 0.00634
hence value of p0.05 > 0.0063,here we reject Ho
ANSWERS
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null, Ho:p=0.14
alternate, H1: p!=0.14
test statistic: 2.73
critical value: -1.96 , 1.96
decision: reject Ho
p-value: 0.00634
we have enough evidence to support the claim that this is significantly different than the prior estimate