Answer: If the level of confidence is increased without changing the sample size then The margin of error will decrease because the critical value will decrease. The decreased margin of error will cause the confidence interval to be narrower.
where;
Margin of error = Critical value × Standard deviation
Here, it can be duly noted that Margin of error has a positive relation with critical value, i.e The margin of error will decrease because the critical value will decrease.
whereas;
The confidence interval is the value ± the margin of error.
Therefore, the decreased margin of error will cause the confidence interval to be narrower.
If the confidence is increased without changing the sample size, The margin of error will increase because the critical value will increase. The increased margin of error will cause the confidence interval to be wider
The margin of error (E) is the amount of error allowed within a sample proportion. It is given by:
[tex]E=z_\frac{\alpha}{2} *\frac{standard\ deviation}{\sqrt{sample\ size} }[/tex]
z is the z score of the confidence level.
Confidence interval = mean ± E
If the confidence is increased without changing the sample size, The margin of error will increase because the critical value will increase. The increased margin of error will cause the confidence interval to be wider
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