Answer: E= 0.107
Step-by-step explanation:
Formula to find the margin of error : [tex]E=z^*\sqrt{\dfrac{p(1-p)}{n}}[/tex]
, where n= sample size .
p= sample proportion
z* = critical value.
Given : Sample size : n= 62
Number of red candies out of 62 = 15
Proportion of red candies = [tex]p=\dfrac{15}{62}\approx0.242[/tex]
We know that , the critical value for 95% confidence = z*= 1.96 [Using z-table]
Then,
[tex]E=(1.96)\sqrt{\dfrac{0.242(1-0.242)}{62}}[/tex]
[tex]E=(1.96)\sqrt{\dfrac{0.242(0.758)}{62}}[/tex]
[tex]E=(1.96)\sqrt{\dfrac{0.183436}{62}}[/tex]
[tex]E=(1.96)\sqrt{0.00295864516129}[/tex]
[tex]E=(1.96)(0.0543934293945)[/tex]
[tex]E=0.106611121613\approx0.107[/tex]
Hence, the margin of error = E= 0.107
