Question

The researcher is deciding between a $95\%$ confidence level and a $99\%$ confidence level. Compared with a $95\%$ confidence interval, a $99\%$ confidence interval will be

a. narrower and would involve a larger risk of being incorrect.

b. wider and would involve a smaller risk of being incorrect.

c. narrower and would involve a smaller risk of being incorrect.

d. wider and would involve a larger risk of being incorrect.

e. wider and would have the same risk of being incorrect.

Short answer

Option (b) is correct.

Step-by-step solution

Given Information

Confidence intervals are$95\%,99\%$

Explanation

Width of confidence interval and confidence level are related positively.

If confidence level is high, degree of precision is higher, risk of being incorrect is lower.

For $99\%$confidence level, interval is wider and risk of being incorrect is lower.

Option (b) is correct.