Question

What happens to the width of a confidence interval for a population mean if the level of confidence is increased without changing the sample size? Assume that the population standard deviation is unknown and the population distribution is approximately normal.
A) 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.B) The margin of error will increase because the critical value will decrease. The increased margin of error will cause the confidence interval to be wider.C) The margin of error will decrease because the critical value will increase. The decreased margin of error will cause the confidence interval to be narrower.D) 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.

Answer 1

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.