Answer :
The 95% confidence interval for the population proportion of members who vote yes is (0.782, 0.818).
What is Random Sample?
A choice that is made at random (purely by chance, with no predictability). They tapes of samples are:
Convenient: Sample taken from a pool that is easily accessible.
Random: Put all the possibilities into a hat, then pull some of them at random. Every kth element is taken in a systematic manner. If you wanted to survey anything on the street, for instance, you may interview every fifth person.
Cluster: The population is divided into groupings, or clusters, and every component of each cluster is surveyed.
Stratified: Additionally stratifies the people into several groupings. But only a small portion of the group is questioned after that.
Now, finding the sample proportion,
[tex]p=\frac{x}{n} \\\\=\frac{1600}{2000}\\\\ =0.8[/tex]
The confidence level is given as,
[tex]C=p\pm[z(\frac{\alpha}{2})\times\sqrt{\frac{p(1-p)}{n} } ][/tex]
The value of [tex]z(\frac{\alpha}{2})[/tex] is 1.96
Putting the values, we get
[tex]C=0.8\pm[1.96\times\sqrt{\frac{0.8(1-0.8)}{2000} } ]\\\\C=0.8\pm[1.96\times\sqrt{\frac{0.8(0.2)}{2000} } ]\\\\C=0.8\pm0.018\\\\C=(0.782,0.818)[/tex]
Therefore, the 95% confidence interval is (0.782,0.818).
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The given question is incomplete. Here is the complete question.
a random sample of 2,000 members of a union reveals that 1,600 would vote yes on a merger proposal. what is the 95% confidence interval for the population proportion of members who would vote yes?
a) 0.782 to 0.818
b) 0.754 to 0.799
c) 0.690 to 0.713
d) 0.799 to 0.951
