Amenican Exceptionalism EXPLO 3.2 The Gallup organization conducted a survey wit

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Amenican Exceptionalism EXPLO 3.2 The Gallup organization conducted a survey with a random sample of 1,019 adult Americans on December 10-12, 2010. They found that 80% of the respondents agreed with the statement that the United States has a unique character that makes it the greatest country in the world 1. Identify the population and sample in this survey Population: Sample 2. Is it reasonable to believe that the sample of 1,019 adult Americans is representative of the larger population? Explnin why or why not. o ent 3. Explain why 80% is a statistic and not a parameter, what symbol would you use to format represent it? Windo Mac. 4. Identify (in words) the parameter that the Gallup organization was interested in estimating. 5. Is it reasonable to conclude that exactly 80% of all adult Americans agree with the state. ment about American exceptionalism? Explain why or why not. 6. Although we expect x to be close to 0.80, we realize there may be other plausible values for the population proportion as well First consider the value of 0.775. Is this a plausible value for ? Use the One Proportion applet to simulate random samples of 1,019 people from such a population. (Hint: Keep in mind that 0.775 is what we are assuming for the population proportion and 0.80 is the observed sample proportion.) What do you esti- mate for the two-sided p-value? Would you reject or fail to reject the null hypothesis at the 5% level of significance? 7. Also check the Summary Stats box and report the mean and standard deviation of this null distribution.

Explanation / Answer

Q6.
Given that,
sample size(n)=1019
success rate ( p )= x/n = 0.8
success probability,( po )=0.775
failure probability,( qo) = 0.225
null, Ho:p=0.775  
alternate, H1: p!=0.775
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=0.8-0.775/(sqrt(0.174375)/1019)
zo =1.9111
| zo | =1.9111
critical value
the value of |z alpha| at los 0.05% is 1.96
we got |zo| =1.911 & | z alpha | =1.96
make decision
hence value of |zo | < | z alpha | and here we do not reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != 1.91111 ) = 0.05599
hence value of p0.05 < 0.056,here we do not reject Ho
ANSWERS
---------------
null, Ho:p=0.775
alternate, H1: p!=0.775
test statistic: 1.9111
critical value: -1.96 , 1.96
decision: do not reject Ho
p-value: 0.05599

we failed to reject the null hypothesis

Q7.
I.
mean = np
where
n = total number of repetitions experiment is excueted
p = success probability
mean = 1019 * 0.8
= 815.2
II.
variance = npq
where
n = total number of repetitions experiment is excueted
p = success probability
q = failure probability
variance = 1019 * 0.8 * 0.2
= 163.04

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