Respuesta :
Answer:
B. Larger sample size and lower confidence level
Step-by-step explanation:
The margin of error of a confidence interval is given by the following formula:
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
z is related to the confidence level. The higher the confidence level, the higher the value of Z.
So, the margin of error is direct proportion to the confidence level and inverse proportional to the sample size.
We want to decrease the margin of error.
So the correct answer is:
B. Larger sample size and lower confidence level
The confidence interval is the interval estimate of an unknown value of an information.
- The option that will make a confidence interval narrower and more precise is B. Larger sample size and lower confidence level
Reasons:
The confidence interval is given by the formula;
[tex]\displaystyle CI=\bar{x}\pm z\frac{s}{\sqrt{n}}[/tex]
Where;
CI = The confidence interval
[tex]\overline x[/tex] = The mean of the sample
z = The given confidence level
s = The sample standard deviation
n = The sample size
Therefore;
- Increasing the sample size, n, reduces the value of [tex]\displaystyle \mathbf{z\frac{s}{\sqrt{n}}}[/tex], and therefore, reduces the confidence interval, making it more precise.
Similarly, we have;
- Reducing the confidence, level, z, reduces the value of [tex]\displaystyle z\frac{s}{\sqrt{n}}[/tex] and therefore, reduces the confidence interval.
The correct option is therefore, B. Larger sample size and lower confidence level.
Learn more here:
https://brainly.com/question/17212516
