Ask Question
19 August, 03:47

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.

+3
Answers (1)
  1. 19 August, 04:03
    0
    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.
Know the Answer?
Not Sure About the Answer?
Find an answer to your question 👍 “What happens to the width of a confidence interval for a population mean if the level of confidence is increased without changing the ...” in 📗 Mathematics if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers