Annette is running against Barry for Mayor of Goatsfield. The local paper takes

Question

Annette is running against Barry for Mayor of Goatsfield. The local paper takes a poll. They record 77 votes for Annette and 64 votes for Barry. a. (Hypotheses) The newspaper would like to predict a winner so they can run a headline declaring the current voter opinion. What are the null and alternative hypotheses for such a test? b. (Model) Write the model that describes the distribution of possible polling results we could have gotten if the null hypothesis were true. c. (Mechanics) Compute the P-value. d. (Conclusion) Come to a conclusion. (Accept/reject Ho and report the paper's decision) (Chapter 20) The 90% confidence interval for Annette's share of the vote is 47.7%, 61.5%). This should be consistent with your answer to (d). Explain the connection

Explanation / Answer

Given that,
sample one, x1 =77, n1 =141, p1= x1/n1=0.546
sample two, x2 =64, n2 =141, p2= x2/n2=0.454
null, Ho: p1 = p2
alternate, annette will win over barry, 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 =(0.546-0.454)/sqrt((0.5*0.5(1/141+1/141))
zo =1.548
| zo | =1.548
critical value
the value of |z | at los 0.05% is 1.645
we got |zo| =1.548 & | z | =1.645
make decision
hence value of |zo | < | z | and here we do not reject Ho
p-value: right tail - Ha : ( p > 1.5483 ) = 0.06078
hence value of p0.05 < 0.06078,here we do not reject Ho
ANSWERS
---------------
a.
null, Ho: p1 = p2
alternate, H1: p1 > p2
b.
z test for diffrence in proportion

test statistic: 1.548
critical value: 1.645
c.
p-value: 0.06078

d.
decision: do not reject Ho

e.
Yes, since the we can't give confirmation on annette win, since CI lower limit lies
below 0.50 and the result is cosistent with option D

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