Respuesta :
Answer:
A. increase the size of the sample.
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 level of [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 width of the interval is given by:
[tex]W = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
So as n(the size of the sample) increases, the width decreases.
If the researchers wanted to decrease the width of the con dence interval, they could
The correct answer is:
Increase n, that is
A. increase the size of the sample.
Option A: Increase the size of the sample.
Given that:
Population size = 1 million
Sample size = 600
Confidence interval(CI) is an interval as the name suggests which has values that are likely to occur with a certain confidence level.
The formula for calculating CI is:
[tex]CI = \overline{x} \pm z\dfrac{s}{\sqrt{n}}\\[/tex]
where the symbols mean:
CI = confidence interval
[tex]\overline{x}[/tex] : sample mean
z = confidence level
s = sample standard deviation
n = size of sample.
To decrease the width, of given CI, we will need to decrease the magnitude of [tex]z\dfrac{s}{\sqrt{n}}[/tex].
For that, as we increase n, the magnitude will automatically go down.
Since n denotes the size of sample, thus we need to increase the size of sample to decrease the confidence interval's width.
Thus option A: increase the size of the sample is correct.
Learn more here:
https://brainly.com/question/2396419
