The confidence interval is given as 0.250 and 0.308
How to solve for the confidence interval?
n = 502
x = 140
x/ n = proportion
= 140/502
= 0.2789
To find the proportion using 85%
1-0.85 = 0.15
0.15/2 = 0.075
Find the z value to be 1.44
[tex]p +- z*\sqrt{p'(1-p')/n\\}\\ = 0.279 +-1.44\sqrt{0.279(1-0.279)/502}[/tex]
= 0.279 +- 0.029
= 0.250, 0.308
Hence the confidence interval is 0.250, 0.308.
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