Respuesta :
Answer:
Explained below.
Step-by-step explanation:
The (1 - α)% confidence interval for the population mean is:
[tex]CI=\bar x\pm z_{\alpha/2}\times\frac{\sigma}{\sqrt{n}}[/tex]
The margin of error for this interval is:
[tex]MOE= z_{\alpha/2}\times\frac{\sigma}{\sqrt{n}}[/tex]
The factors affecting the MOE are:
- The sample size (n) is inversely proportional to the MOE, thus increasing n decreases the MOE and vice-versa.
- Variance (σ²) is the square of S.D. So if we increase σ² then σ increases. Since σ is directly proportional to MOE, increasing σ increases MOE.
- The confidence level is the value of (1 – α). If we increase the confidence level then the critical value increases and thus MOE also increases.
Since the population standard deviation is not provided it is obvious the sample standard deviation is used to estimate the value of σ.
On increasing the value of σ the MOE will also increase.
As the sample size is inversely proportional, increasing the sample size by a factor of 4 will reduce the margin of error by half. But since σ is also increasing there are two factors affecting the MOE together.
Therefore reducing the MOE by more than half the original value.
