Question

When one increases the confidence level (1-α), say from 0.90 to 0.95, what happens to the width of the confidence interval? a. It stays the same b. It becomes wider c. It becomes narrower

Answer 1

Step-by-step explanation:

A higher confidence interval means less power which in turns means a smaller rejection religion.So our confidence interval would become wider.

Answer 2

(option B) The width of the confidence interval increases when the confidence level is raised from 0.90 to 0.95 because a higher confidence level requires a larger error bound to maintain the increased certainty.

Step-by-step explanation:

When the confidence level increases from 0.90 to 0.95, the width of the confidence interval (option B) becomes wider. This is because a higher confidence level means you want to be more certain that your interval will capture the true population parameter. As a result, the error bound for the mean increases, as we are including a larger area under the normal distribution curve for our interval calculation.

If all other factors such as the sample mean, standard deviation, and sample size remain constant, increasing the confidence level from 0.90 to 0.95 requires a larger error bound on the estimate to maintain the higher level of confidence. This expanded error bound translates into a wider confidence interval.

For example, a dataset with a 90 percent confidence interval might have an interval of (67.18, 68.82). If the confidence level is increased to 95 percent, assuming all else remains unchanged, the interval might become (67.02, 68.98), demonstrating a wider range due to increased certainty.