Voters in a particular city who identify themselves with one or the other of two
ID: 3173230 • Letter: V
Question
Voters in a particular city who identify themselves with one or the other of two political parties were randomly selected and asked if they favor a proposal to allow citizens with proper license to carry a concealed handgun in city parks. The results are: a. Give a point estimate for the difference in the proportion of all members of Party A and all members of Party B who favor the proposal. b. Construct the 95% confidence interval for the difference, based on these data. c. Test, at the 5% level of significance, the hypothesis that the proportion of all members of Party A who favor the proposal is less than the proportion of all members of Party B who do. d. Compute the p-value of the test.Explanation / Answer
a.
point estimate for diffrence of proportion = (0.6-0.7) = 0.1
b.
Confidence Interval for Diffrence of Proportion
CI = (p1 - p2) ± Z a/2 Sqrt(p1(1-p1)/n1 + p2(1-p2)/n2 )
Proportion 1
No. of chances( X1 )=90
No.Of Observed (n1)=150
P1= X1/n1=0.6
Proportion 2
No. of chances(X2)=140
No.Of Observed (n2)=200
P2= X2/n2=0.7
C.I = (0.6-0.7) ±Z a/2 * Sqrt( (0.6*0.4/150) + (0.7*0.3/200) )
=(0.6-0.7) ± 1.96* Sqrt(0.0027)
=-0.1-0.1009,-0.1+0.1009
=[-0.2009,0.0009]
c.
Given that,
sample one, x1 =90, n1 =150, p1= x1/n1=0.6
sample two, x2 =140, n2 =200, p2= x2/n2=0.7
null, Ho: p1 > p2
alternate, H1: p1 < p2
level of significance, = 0.05
from standard normal table,left tailed z /2 =
since our test is left-tailed
reject Ho, if zo < -1.645
we use test statistic (z) = (p1-p2)/(p^q^(1/n1+1/n2))
zo =(0.6-0.7)/sqrt((0.657*0.343(1/150+1/200))
zo =-1.95
| zo | =1.95
critical value
the value of |z | at los 0.05% is 1.645
we got |zo| =1.95 & | z | =1.645
make decision
hence value of | zo | > | z | and here we reject Ho
p-value: left tail - Ha : ( p < -1.9505 ) = 0.02556
hence value of p0.05 > 0.02556,here we reject Ho
ANSWERS
---------------
null, Ho: p1 = p2
alternate, H1: p1 < p2
test statistic: -1.95
critical value: -1.645
decision: reject Ho
p-value: 0.02556
we have evidence that proportion of all members of Party A who
favor the proposal is less than the proportion of all members of Party B
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