Using the margin of error, it is found that the effect of this increase is to reduce the variability.
Confidence interval of proportions and margin of error
- In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
- In which z is the z-score that has a p-value of [tex]\frac{1+\alpha}{2}[/tex].
The margin of error of the interval is given by:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
- For it, it can be seen that M and n are inversely proportional, that is, a higher sample size leads to a smaller margin of error and consequently, less variability.
- Hence, the effect of this increase is to reduce the variability.
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