Respuesta :
The following relation can be used to show the relationship between the confidence level and the sample size
[tex]\begin{gathered} \bar{\text{confidence interval(C.I)=}}\bar{x}\pm MOE \\ \text{where,} \\ \text{MOE}=\text{Margin of error} \end{gathered}[/tex]Also,
[tex]\text{MOE}=C.I\times S\tan dard\text{ error(S.E)}[/tex]And,
[tex]\begin{gathered} S\mathrm{}E=\frac{r}{\sqrt[]{n}} \\ \end{gathered}[/tex]There fore,
when the value of n is large, the standard error will be low
when the standard error is low margin of error(MOE) will also be low
Hence, if the Margin of error the confidence level will have a larger width
Therefore,
We can say that A confidence level would have a larger width with a small sample size from normal distribution
Final answer is OPTION A
