Question

Which confidence interval would have a larger width: A confidence interval using a large sample size or a confidence interval using a small sample size from a normal distribution?A) confidence interval with small sample size from normal distributionB) Confidence interval with large sample size

Answer 1

The following relation can be used to show the relationship between the confidence level and the sample size

`\begin{gathered} \bar{\text{confidence interval(C.I)=}}\bar{x}\pm MOE \\ \text{where,} \\ \text{MOE}=\text{Margin of error} \end{gathered}`

Also,

`\text{MOE}=C.I* S\tan dard\text{ error(S.E)}`

And,

`\begin{gathered} S\mathrm{}E=\frac{r}{\sqrt[]{n}} \\ \end{gathered}`

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