Answer:
The sample size 'n' =15
Step-by-step explanation:
Explanation:-
given data A newspaper article about the results of a poll states: "In theory, the results of such a poll, in 99 cases out of 100
Sample proportion 'p' = 99/100 =0.99
Given Margin of error = 5% =0.05
The margin of error is determined by
[tex]M.E = \frac{Z_{\frac{\alpha }{2} }\sqrt{p(1-p)} }{\sqrt{n} }[/tex]
The Z-score of 95% of level of significance
[tex]Z_{\frac{0.05}{2} } = Z_{0.025} =1.96[/tex]
[tex]0.05 =\frac{1.96 X \sqrt{0.99(0.01)} }{\sqrt{n} }[/tex]
Cross multiplication, we get
[tex]\sqrt{n} =\frac{1.96 X \sqrt{0.99(0.01)} }{0.05 }[/tex]
[tex]\sqrt{n} = 3.90[/tex]
Squaring on both sides, we get
n = 15.21
Final answer:-
Sample size 'n' = 15
