If you determine a confidence interval for a population proportion to be .65 to .75 with an α = .04, what happens to the interval if the level of significance is decreased?

When you decrease the level of significance (α) in constructing a confidence interval, you are essentially increasing the confidence level. For example, if you move from a significance level of 0.04 to a lower significance level, say 0.01, you are asserting more confidence that the true population parameter falls within the calculated interval.

To achieve this increased confidence level, the interval must be widened. This is because a wider range of values is required to maintain a higher degree of certainty that it captures the true population proportion. In practical terms, as the confidence level increases, you are allowing for a larger range in your estimate to ensure that you do not mistakenly exclude the true parameter value.

Therefore, when the level of significance decreases, the confidence interval for the population proportion indeed becomes wider to reflect greater certainty about the estimate. The increased width of the interval is a direct response to the need for more assurance that the true proportion is encapsulated within those limits.