In: Statistics and Probability
A research institute poll asked respondents if they felt vulnerable to identity theft. In the poll, n = 1046 and x = 584 who said "yes." Use a 99% confidence level.
Level of Significance, α =
0.01
Number of Items of Interest, x =
584
Sample Size, n = 1046
Sample Proportion , p̂ = x/n =
0.558
z -value = Zα/2 = 2.576 [excel
formula =NORMSINV(α/2)]
Standard Error , SE = √[p̂(1-p̂)/n] =
0.0154
margin of error , E = Z*SE = 2.576
* 0.0154 = 0.0396
99% Confidence Interval is
Interval Lower Limit = p̂ - E = 0.558
- 0.0396 = 0.5188
Interval Upper Limit = p̂ + E = 0.558
+ 0.0396 = 0.5979
99% confidence interval is (
0.5188 < p < 0.5979
)
Please revert in case of any doubt.
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