A recent poll was conducted by the Pew Research center between April 7th and Apr

Question

A recent poll was conducted by the Pew Research center between April 7th and April 11th, 2017. A total of 1,501 adults living in the 50 U.S. states and the District of Columbia (aged 18 and older) were randomly selected using a quota sampling method with random digit dialing and were interviewed over the phone (either landline or cell phone). 871 (58%) of the sampled adults approved of the U.S. missile strikes against Syria in response to reports of the use of chemical weapons by Bashar al-Assad’s government. Assume we want to make an inference on all adults living in the 50 U.S. states and District of Columbia (aged 18 and older). [http://www.people-press.org/2017/04/12/public-supports-syria-missile-strikes-but-few-see-a-clear-plan-for-addressing-situation/]

a) Define the parameter of interest in the context of the problem (include the symbol used to denote it).

b) What is the statistic in this problem (include the symbol used to denote it)?

c) Check the assumptions necessary to construct a normal-based confidence interval for the parameter of interest by verifying the appropriate conditions. Actually show that you checked these in the context of the problem.

d) Find the margin of error if we want 95% confidence in our estimate of the parameter of interest.

e) Find the 95% confidence interval for the parameter of interest.

f) In the context of the problem, give a conclusion based on the confidence interval you found in part e. Your sentence should start with the words “We are 95% confident that……”

Explanation / Answer

Part-a

Parameter of interest is p, the proportion of adults approved of the U.S. missile strikes against Syria in response to reports of the use of chemical weapons by Bashar al-Assad’s government.

Part-b

Test statistic is Z =(phat-p0)/sqrt(p0*(1-p0)/n) , where p0 is the proportion under null hypothesis, phat is sample proportion and n is sample size.

Part-c

WE have np=871>5 and n(1-p)=1501-871=630>5 , so assumption necessary to construct a normal-based confidence interval for the parameter of interest is satisfied.

Part-d

Critical z=1.96

Margin of error ME=z*sqrt(phat*(1-phat)/n)

=1.96*sqrt(0.58*(1-0.58)/1501)

=0.0250

Part-e

95% confidence interval of p is =phat-ME, phat+ME

=0.58-0.0250 , 0.58+0.0250

=(0.555                 0.605)

Part-f

We are 95% confident that this interval contains the true population proportion of adults approved of the U.S. missile strikes against Syria in response to reports of the use of chemical weapons by Bashar al-Assad’s government

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