A survey found that 79% of a random sample of 1024 Canadian adults approved of cloning endangered animals.Find the margin of error for this survey if we want 90% confidence in our estimate of the percent of Canadian adults who approve of cloning endangered animals.

A) 4.56%
B) 21.4%
C) 5.43%
D) 2.49%
E) 2.09%

Question

Chrissean Rodriguez · Accepted Answer

Final Answer : E, Explanation :   The margin of error (ME) for a proportion can be calculated using the formula:   M E = Z ∗ p ( 1 − p ) n ME = Z * \sqrt{\frac{p(1-p)}{n}} ME = Z ∗ n p ( 1 − p ) ​ ​  , where   Z Z Z   is the Z-score corresponding to the desired confidence level,   p p p   is the sample proportion, and   n n n   is the sample size. For a 90% confidence level, the Z-score is approximately 1.645. Given   p = 0.79 p = 0.79 p = 0.79   and   n = 1024 n = 1024 n = 1024  , the calculation is as follows:   M E = 1.645 ∗ 0.79 ( 1 − 0.79 ) 1024 ME = 1.645 * \sqrt{\frac{0.79(1-0.79)}{1024}} ME = 1.645 ∗ 1024 0.79 ( 1 − 0.79 ) ​ ​  , which equals approximately 0.0209 or 2.09%.

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