Hypothesis testing two proportions (15 points) In March 2003, the Pew Research G

Question

Hypothesis testing two proportions (15 points) In March 2003, the Pew Research Group surveyed 1508 adults Americans and asked, "Do you believe the USA was right or wrong to in using military force against Iraq?" Of the 1500 adults surveyed, 1050 stated the USA made the correct decision. In august of 2017, the Pew Research group asked the same question to 1245 adult Americans and found that 820 still share the same opinion as in 2003. Is there significant evidence to support the claim that this proportion is lower now than it was in 2003? Use alpha = 0.01 Set up the Hypotheses and indicate the claim (2.5 points) Ho: Ha: Decision rule (In complete sentence for 2.5 points) a. b. c. Computation (5 points)

Explanation / Answer

Given that,
sample one, x1 =1050, n1 =1500, p1= x1/n1=0.7
sample two, x2 =820, n2 =1245, p2= x2/n2=0.659
null, Ho: p1 = p2
alternate, H1: p1 < p2
level of significance, = 0.01
from standard normal table,left tailed z /2 =2.326
since our test is left-tailed
reject Ho, if zo < -2.326
we use test statistic (z) = (p1-p2)/(p^q^(1/n1+1/n2))
zo =(0.7-0.659)/sqrt((0.681*0.319(1/1500+1/1245))
zo =2.315
| zo | =2.315
critical value
the value of |z | at los 0.01% is 2.326
we got |zo| =2.315 & | z | =2.326
make decision
hence value of |zo | < | z | and here we do not reject Ho
p-value: left tail - Ha : ( p < 2.3153 ) = 0.9897
hence value of p0.01 < 0.9897,here we do not reject Ho
ANSWERS
---------------
a.
null, Ho: p1 = p2
alternate, H1: p1 < p2
test statistic: 2.315
critical value: -2.326
b.
decision: do not reject Ho
p-value: 0.9897

c.
we do not have enough evidence to support the claim that this proportion is lower than this was in 2003

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