Thus the correct answer is 6.30% < p < 12.2%
Given,
[tex]p = 0.0927[/tex]
[tex]q= 1 - p\\= 1 - 0.0927 \\q= 0.9073[/tex]
[tex]n = 259\\c = 90%[/tex]
The Z critical value for [tex]C[/tex] = 90% is 1.645
The formula of confidence interval is,
[tex]p-\sqrt{p} \frac{q}{n} ,p+z\sqrt{p} \sqrt{p} \frac{q}{n}[/tex]
Substitute the given values into the above value we get,
[tex]0.0927-1.645\sqrt{0.0927} \frac{0.9073}{259},0.0927+1.645\sqrt{0.0927}\frac{0.9073}{259} \\ =0.0927 - 0.02964, 0.0927 + 0.02964\\=0.0630, 0.1223[/tex]
Hence in terms of percent it becomes,
(6.30% , 12.23%)
That is 6.30% <p<12.23%
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