Question

for the same sample statistics, which level of confidence would produce the widest confidence interval? explain your reasoning. choose the correct answer below. 90%, because as the level of confidence decreases, ( z_c ) increases. 90%, because as the level of confidence decreases, ( z_c ) decreases. 99%, because as the level of confidence increases, ( z_c ) increases. 99%, because as the level of confidence increases, ( z_c ) decreases.

Explanation:

The formula for a confidence interval (for example, for a population mean when the population standard deviation \(\sigma\) is known) is \(\bar{x}\pm z_{c}\frac{\sigma}{\sqrt{n}}\). The width of the confidence interval is \(2\times z_{c}\frac{\sigma}{\sqrt{n}}\). As the confidence level increases, the value of \(z_{c}\) (the critical value) increases. A higher \(z_{c}\) value leads to a wider confidence interval.

Answer:

99%, because as the level of confidence increases, \(z_{c}\) increases.