Respuesta :
Answer:
b. It will decrease by a factor of 2
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence interval [tex]1-\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 zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The lower end of the interval is given by:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The upper end of the interval is given by:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The length of the interval is the subtraction of the upper end by the lower end, so it is:
[tex]L = 2z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
This means that the length is inverse proportional to the square root of the size of the sample.
So, if the sample size is multiplied by 4, the length of the interval is going to decrease by a factor of 2.
